So I recently found out about the Sierpinski triangles and decided to code it up myself because it seemed like a fun thing to do.
The original algorithm is as familiar:
- Take three points in a plane to form a triangle, you need not draw it.
- Randomly select any point inside the triangle and consider that your current position.
- Randomly select any one of the three vertex points.
- Move half the distance from your current position to the selected vertex.
- Plot the current position.
- Repeat from step 3.
What I instead did on step 4 just to try and spice things up was to calculate $x'= (x_{2} - x_{1})/2$ and $y' = \frac{\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}}{2}$ and ended up with the following result.
This is absolutely unexpected and beautiful. I have tried Googling around but have yet to find anyone mentioning this fractal. I just wanted to share this cool and beautiful fractal.
Zooming in we see another pair of birds
Yet another zoom in...
