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Generative Geometry
Generative Geometry is the computational creation of shapes, patterns, motions and forms through mathematical rules instead of manual drawing.
A single formula can generate thousands of visual outcomes — evolving like biological DNA, but in digital space.
Funebra treats Generative Geometry not only as mathematical output, but as living structure composed of bn-points, rulesets, and transformations.
Instead of drawing a circle, we define it:
x = cos(o) * r
y = sin(o) * r
Change r, modulate o, repeat → the form mutates.
A bn-point is the smallest Funebra-unit — similar to a pixel, vertex, and creature combined.
Properties include:
| Property | Meaning |
|---|---|
| id:bn# | Unique point identity |
| x,y | Position in space |
| symbol/color | Visual expression |
| function link | Ability to react, move, evolve |
A shape = a network of bn-points behaving as one organism.
Math → Points → Patterns → Life-like behavior
If rules change over time, geometry becomes dynamic rather than static.
x = cos(o * 5) * 120
y = sin(o * 5) * 120
Small rule change → radical shape change.
x = (a + b*cos(k*o)) * cos(o)
y = (a + b*cos(k*o)) * sin(o)
z = b*sin(k*o)
With values of a, b, k the geometry folds into knots, rings, toroids, DNA-like helices.
Generative Geometry enables:
✔ Infinite variation from finite math
✔ Procedural art, 2D/3D scenes, animations
✔ Physics simulations & biological modeling
✔ Emergent complexity — order from equations
✔ Bridges between art, physics, intelligence, life
Human creativity becomes a rulesmith, not just an illustrator.
Funebra research explores the idea that:
If geometry can generate itself,
then geometry can evolve.
bn-points may one day behave like digital DNA, forming shapes that learn, grow, and respond — a foundation for future Hybrid Advanced Intelligence (HAI).