Fractals of the Mandelbrot Set.

These images are primarily based on the Mandelbrot and Julia sets. The underlying math expressions for these sets are deceivingly simple for such complex and subtle structures.

Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.

$Image 10375, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10368, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10369, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10370, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10371, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10372, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10373, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10374, The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10376, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10377, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10378, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10379, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10380, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10381, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10382, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10383, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10384, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10385, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10386, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10387, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10388, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10389, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10390, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10391, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10392, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10393, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10394, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10395, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10396, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10397, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10398, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10399, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10400, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10401, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10402, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10403, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10404, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10405, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10406, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10407, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10408, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10409, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10410, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10411, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10412, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10413, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10414, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10415, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10416, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10417, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10418, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10419, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10420, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10421, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10422, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

$Image 10423, Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set., Mandelbrot set, Copyright © Phillip Colla, all rights reserved worldwide. Keywords: abstract:abstracts and patterns:fractal:fractal detail:fractal picture:mandelbrot fractal:mandelbrot set.$

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