The Sierpinski Triangle is a fractal. According to Wikipedia it was named after "mathematician Waclaw Sierpinski who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral of Anagni, Italy." You can create the Sierpinski Triangle (and very similar fractals) with surprisingly little code. The following picture and instructions are also from Wikipedia.

Start with any triangle, though the usual Sierpinski triangle uses an equilateral triangle. Shrink the triangle to ½ height and ½ width, make three copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner (image 2). Note the emergence of the central hole - because the three shrunken triangles can between them cover only 3/4 of the area of the original. (Holes are an important feature of Sierpinski's triangle.) Repeat step 2 with each of the smaller triangles (image 3 and so on).

1. You may find slides in the Recursion presentation helpful.

2. Fork and clone down this repository.

3. Write the sierpinski function:

   • If len is less than or equal to 20 (or some variable)
     • Draw a triangle with the left corner at (x,y) and a base and height equal to len.
   • else
     • recursively call the sierpinksi function to draw a triangle with the left corner at (x,y) and a base and height equal to len/2.
     • Again, call the sierpinksi function a second time to draw another triangle a distance of len/2 to the right of the first triangle.
     • Now, call the sierpinksi function a third time to draw a triangle a distance of len/4 to the right and len/2 up from the first triangle. This triangle should "sit on top" of the first two.

4. Once you have the sierpinksi function completed, call it once in draw() to start the process. You can change the number and size of the triangles by changing the base case limit in the if from 20 to some variable and adjusting the value of the variable. Some ways to make the program interactive include using mousePressed(), keyPressed(), mouseDragged() or mouseMoved() to change the base case limit.

5. Feel free to create your own individual variation of the Sierpinski triangle. Your recursive triangle doesn't have to look like any other. It doesn't even need to use triangles. The mathematically adventurous might want to check out the sierpinski triangle page to end most sierpinski triangle pages ™.

6. You could also create a Sierpinski carpet, Wallis sieve, Hawaiian earring, Menger sponge or similiar as an alternative to the Sierpinski Triangle.