DeepDream Field (Mike Tyka — AI: DeepDream / Inceptionism)

Math essence

F: (H,W,3) → (H,W), F(I) = max(Σ_k a_k·sin(k_x·R_θx + k_y·R_θy + φ_k)·gray(I) - τ, 0). Update: I ← I + α·∇Σ F(I) computed by central differences on a subsampled grid (stride = D/32). Zoom: I ← zoom_resample(I, zoom). Phase drift: φ_k ← φ_k + 0.07 each step.

Parameters

Reference

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

"""TykaDeepDreamField — Mike Tyka "iterative DeepDream" kernel.

Mike Tyka, alongside Alexander Mordvintsev and Christopher Olah,
co-created Google's DeepDream (2015) and the *Inceptionism: Going
Deeper into Neural Networks* blog post.  Tyka's artistic method,
applied to the *AI: DeepDream* series (2015-): take a starting image,
pick a layer of a pretrained convnet, and *iteratively* perform
gradient ascent on the image to maximize the L2 norm of that layer's
activations — then zoom in and repeat.  Lower layers yield geometry
and edges; higher layers hallucinate whole creatures.  The image
grows fractal, self-similar detail forever.

We replicate the algorithmic kernel in numpy by simulating the
"maximize a synthetic feature response" loop:
  1. Build a synthetic 2-channel "feature map" F from layered
     sinusoids at multiple scales.
  2. Start with a noise image I.
  3. At each step: compute R = ‖F(I)‖_2 (a scalar feature response),
     compute its gradient w.r.t. I via central differences, update
     I ← I + α·∇R (gradient ascent).
  4. Apply a ReLU-like threshold nonlinearity to R periodically so
     "weak features" get pruned (mimicking ReLU in the convnet).
  5. Repeat, with mild image zoom-and-resample so features become
     self-similar across scales (Tyka's "fractal DeepDream").
  6. Render the amplified image.

References:
- https://www.miketyka.com/
- https://aiartists.org/mike-tyka
- https://artsandculture.google.com/story/deepdream-the-art-of-neural-networks-gray-area/gAVBUUSCYZ_FNQ
- Mordvintsev, Tyka, Olah — "Inceptionism: Going Deeper into Neural
  Networks" (Google Research blog, 2015).
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


class TykaDeepDreamField:
    """Iterative synthetic-feature amplification — Tyka's DeepDream kernel.

    Parameters
    ----------
    dim : int
        Square canvas side length (px).
    n_iter : int
        Number of inner gradient-ascent iterations per ``step`` call.
    step_size : float
        α — gradient ascent learning rate.
    feature_freq : float
        Spatial frequency of the dominant feature sinusoid.
    n_octaves : int
        Number of summed sinusoidal octaves in the feature map.
    threshold : float
        ReLU-like threshold for the feature response (0 disables).
    zoom : float
        Per-step fractional zoom-and-resample (Tyka's fractal zoom).
    seed_image : str