Draw a Sierpinski Gasket / Triangle – slower movements work best. Left click / tap 2 fingers to enter ‘Modulo Mode’ or right click / tap 3 fingers to reset the generator.
Sierpinski triangle can be constructed through a number of different mathematical methods, however the most enjoyable is to draw it with pen and paper:
1. Draw a triangle.
2. Subdivide into four smaller triangles (split the edges of the first triangle)
3. Ignore the central triangle(s).
3. Repeat step 2 for the remaining triangles.
The Sierpinski pattern seen here is produced by simply marking all odd numbers in Pascal’s triangle. You can experience this for yourself by writing out Pascal’s triangle and circling odd numbers – give it a go. The ‘modulo mode’ takes this concept a step further. Rather than just marking odd numbers white and even numbers black – the colors are given by applying the modulo operation. The modulo is the remainder of a number after it has been divided by another. The ‘Modulo Number’ option in the control panel sets this dividing number (the default is 5). Experiment with different values: What are qualitative differences between the patterns? Are there discernible ‘families’ of patterning? How does this inform out relationship with numbers?