Dynamic Math Objects

Dynamic Math Objects are evolving, algorithm-driven geometries within the Funebra Math-Art Engine — objects that behave like miniature mathematical life-forms.

They move, mutate, remember, orbit, and sometimes emerge into entirely new structures, as if driven by internal logic.

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🔥 Defining Characteristics

Property | Meaning | Example Behavior -- | -- | -- Autonomy | Object acts without constant input | Self-oscillation, drift Responsiveness | Reacts to environment | Cursor gravity, audio beats Mutation | Actively transforms form | Circle → Flower → Torus Memory | Shape influenced by past state | Trails, history shadows Emergence | New structure forms from rules | Particle → organism-like growth

Funebra.Dynamic({
  seed: 2741,
  points: 96,
  evolve(v){
    this.r += Math.sin(v/20) * 2;   // breathing radius
    this.a += 0.02;                 // rotation
  }
});

Dynamic objects don’t exist only in space —
they exist in time.

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🧠 Conceptual Model

Input → (Math Core) → Output
       ↘ Memory ↗

A Dynamic Object is both what it is now and what it was before.

It grows from frames like a plant grows from cells.

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📈 Four Main Classes

1) Oscillator Objects

Breathing forms, smooth like waves.
Perfect for rhythmic math-life behaviors.

radius = base + sin(t * φ) * Δ

2) Morphing Structures

Shapes that inherit parameters from previous forms.

Example evolution chain:

Circle → Triangle → Star → Flower → Unknown

3) Emitters & Streamers

These give birth to new bn-points.
They can leave trails, sparks, falling particles.

if(t % 6 == 0) spawnPoint();

4) Self-Orbitals

Orbit-in-orbit — fractal celestial bodies.

planet rotates center
moon rotates planet
ring rotates moon

Systems like these mimic solar dynamics.