Here’s another example of detail within the Mandelbrot fractal set, illustrated by assigning color to the number of iterations required for the expression to explode:
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.
Image ID: 18729
Species: Mandelbrot Fractal, Mandelbrot set