You can choose among several shading methods. However, when the point is inside or outside the region, the iterations produce very simple curves. If the point is close to the boundary of the region, many iterations are performed and form a repeating pattern, but they stay within a fixed distance of the origin. ![]() The image below illustrates the different behavior of the iterations depending on where the point is in UV space. Otherwise, if the value exceeds the escape radius, it is outside of the region. If the value stays within the escape radius, regardless of the number of iterations, it is in the region. In other words, if you have a point in UV space, and you want to determine if the point is inside the region or not, you iterate the function at that point (that is, take the output of the function and apply the function again repeatedly) and examine its value. ![]() ![]() It represents the region of the complex plane z n+1 = z n 2 + c, where you start with z 0 = 0 and iterate repeatedly while the absolute value of z n remains bounded. The Mandelbrot (and its related sets) evaluations are based on iteration.
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