Fractal Stars
One rule. Start from a point. Place its children evenly on a circle around it, one step away. Then treat every child as a parent and repeat, with the step shrunk and the whole generation turned. Four numbers decide everything — and they are enough for a Sierpiński triangle, Koch's snowflake, a golden-section triangle, a double-tailed dragon, a peacock and eleven more.
Romanesco. Every floret is a smaller copy of the head. Nothing in the plant knows what the whole is shaped like — it only knows the rule.
The four numbers
| Children | how many points spawn from each — the symmetry. 1 gives a spiral, 2 a curve, 3+ a star |
| Generations | how many times the rule is applied |
| Step factor | how fast the step shrinks — below 1 it converges |
| Deflection | how far each generation twists against its parent |
The sixteen figures carry their exact constants (⅓, (√5−1)/2, (√6−√2)/2), so Koch and Sierpiński come out precise rather than approximately right — round any of them and the sub-figures stop meeting.
Try it
- 🌿 Open the figures — one screen: a figure drawing itself, its four numbers under it, and the sixteen a click away. Change a number, press Draw, watch what it was holding together.
- 📖 How it works — the rule, the constants, and what came from where.
Rebuilt from the Systemorph Cloud Fractal Stars notebook as a MeshWeaver node type: the parameters are node content, the figure is derived on every render, and the maths is plain C# the mesh compiles live and tests on every build.