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.

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.

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.

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.

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.

Fractal design. 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.

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.

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.

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.

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.

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.

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.