How it works:
- Start with a triangle and a random point inside it.
- Repeatedly:
- Select a random vertex of the triangle
- Draw a point halfway between the current point and the selected vertex
- Use this new point as the starting point for the next iteration
- As this process continues, the Sierpinski Triangle fractal pattern emerges.
Why it's interesting:
This demonstrates how complex patterns can emerge from simple rules and randomness. Similar phenomena occur in nature, such as:
- Snowflake formation
- Plant growth patterns (e.g., ferns, romanesco broccoli)
- River networks and drainage patterns
- Lightning branching
- Crystal growth
- Galaxy formation
These phenomena, like the Sierpinski Triangle, exhibit complex structures that emerge from simple underlying processes, illustrating how order can arise from chaos.