- Michael Ortiz
This variation of the Sierpinski triangle provides a simplified example of how ideas from fractal geometry can be used to render terrain in video games and CGI-enhanced movies. The construction differs from that of the Sierpinski triangle in that, at each step, instead of the midpoint of each side, a random point in a specified neighborhood of the midpoint is selected. In this applet the radius of the neighborhood is 20% of the given side. In real life many more complicating factors go into producing realistic terrain, but the basic principle is the same. Clicking the reset icon will render a new "Matterhorn." The slider switches between iterations, varying from the input (a triangle) to the seventh iteration. The final construction has 3,280 triangles, so it may take a moment to load up and refresh.