How to Build a Simple Recursive Geometry Engine Using Only One Rule

Grasshopper
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1

Here’s the minimal framework:

  1. Choose a base shape S0.
    It can be anything — a line, a triangle, a curve, even a symbolic object.

  2. Define one transformation rule T.
    This rule can scale, rotate, subdivide, distort, or otherwise modify the shape.

  3. Apply it repeatedly:
    S(n+1) = T(Sn)

With just that, you can generate surprisingly complex behavior. Some systems stabilize, some explode, some fold into attractors, and some reveal hidden symmetry.

2

Uh, okay.