Style Transfer Field (Gene Kogan — ml4a)

Math essence

F(x,y) = Σ_k a_k · sin(k_x · R_θ·x + k_y · R_θ·y + φ_k·(1+0.3k)); ∇F computed by central differences and unit-normalised. Agent update: v ← momentum·v + speed·∇F(F(p)) + jitter; p ← p + v (mod dim). Deposit HSV-coloured trail at p. Every impulse_period steps: canvas += α·tint(F); canvas *= fade.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/ml_artists/KoganStyleTransferField/reference.py

"""KoganStyleTransferField — Gene Kogan (ml4a) "style transfer field" kernel.

Gene Kogan's *Experiments with Style Transfer* (and the broader ml4a
curriculum at ml4a.github.io) treats neural style transfer as a
*gradient-ascent* procedure: an output image is iteratively updated
so its feature activations at chosen convnet layers match those of a
style reference, while keeping activations at content layers close to
a content reference.  The "field" we extract from this idea is the
gradient of the *Gram-matrix style loss* with respect to the input
image — a vector field over the canvas that, when followed, *increases
style-ness* of the image.

We translate the kernel to numpy:
  1. Build a synthetic multi-octave "neural feature map" F(x, y)
     using summed sinusoids with a couple of spatial frequencies and
     a slow phase drift.
  2. Compute its (x, y)-gradient as a smooth vector field
     (∇F) using a Sobel filter.
  3. Spawn N agents that follow the gradient (with momentum, jitter
     and wrap-around), depositing a fading coloured trail on the
     canvas as they go.
  4. Optionally inject a "neural style impulse" — every K steps, add
     a soft texture boost derived from F itself, mimicking the way
     style transfer updates affect the rendered image.

References:
- https://ml4a.github.io/ml4a/style_transfer/
- https://genekogan.com/works/style-transfer/
- https://genekogan.com/
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


class KoganStyleTransferField:
    """Flow field driven by gradients of a synthetic neural feature map.

    Parameters
    ----------
    dim : int
        Square canvas side length (px).
    n_agents : int
        Number of trail-following agents.
    feature_scale : float
        Spatial frequency of the dominant feature map (cycles per dim).
    n_octaves : int
        Number of summed sinusoidal octaves in F.
    feature_drift : float
        Per-step phase drift of F (radians per step, total).
    speed : float
        Step length per agent per step.
    momentum : float
        Velocity retention (0..1).
    trail_alpha : float
        Canvas deposit opacity per agent per step.
    impulse_period : int
        Number of steps between "neural style impulses" (texture boosts).