What We Do
Click the images below to run the programs.
The Koch Snowflake is interesting because while the bounded area is finite, the border length is infinite. The program below adds noise as it plots the points to make it look a bit more geographic.
The Barnsley Fern just takes a point and puts it through one of four transforms that involve translating, scaling, and rotating over and over and over. The result looks awfully like a real fern!
The second fern program below shows the four transformations as little boxes made by transforming the points (0, 0), (0, 1), (1, 1) and (1, 0) and then connecting them with lines. It adds a little random noise to the parameters to create different shapes of ferns.
The Sierpinski Triangle puts a point through one of three transformations that scale it from a big triangle to one of three small triangles at its points. (The code works though by moving the current point halfway towards one of the corners of the triangle.) The program below shows how the points are evenly distributed. I didn't expect that!
And then there is the famous Mandelbrot Set. The algorithm is based on scanning an array to find points in the set. This is unsatisyfing. It would be more interesting to search for a a border point and then to search locally for other border points until the boundary were drawn.
The Koch Snowflake.
The Barnsley Fern.
The Barnsley Fern with noise.
The Sierpinski Triangle.
The Mandelbrot Set.