Affine IFS Point-Set Fitting

Backend

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Model

K (transforms)

N (depth)

Enumeration

orbit size: ?

Optimizer

algorithm

learning rate

steps / click

fps cap

Loss

α (P→Q)

β (Q→P)

Regularizers

λ_A (||A||²_F) λ_b (||b||²) contractivity penalty (||A||_F ≤ √2(1-ε))

weight

Initialization

random seed

Run

Loss curve

Transforms θ

target Q

orbit P_N(θ)

fixed points + A·ê basis (image of unit square)

Notes

Each transform is T_k(x)=A_k x + b_k in ℝ². The orbit P_N(θ) is the set of points obtained by applying length-N words (commutative ↔ multiset) starting from 0. Loss is symmetric Chamfer (squared NN distance). Gradients flow through TensorFlow.js autodiff. Frozen transforms are held constant — their gradients are masked to zero before the optimizer step.