NoiseNCA: Noisy Seed Improves Spatio-Temporal Continuity of Neural Cellular Automata

In addition to the common interactive controls in NCA models such as Cell Alignment and Rotation, and Regeneration Brush, NoiseNCA allows continuous control over the rate of pattern formation and the scale of the synthesized pattern using the $\Delta t$ and $(\Delta x, \Delta y)$ sliders, respectively.

Steps / Frame:

$\Delta x = $
$\Delta y = $

Brush Size

$\Delta t = $

Cell Alignment

Rotation:

Resolution:

Click or tap the image to erase parts of the pattern.

When changing $(\Delta x, \Delta y)$, we automatically adjust the value of $\Delta t$ to avoid the Euler integration from overshooting.
In the Isotropic mode, the scaling factors are forced to be equal $\Delta x = \Delta y$.

Target Appearance

Multiscale Video

By varying the value of $(\Delta x, \Delta y)$ across the image, NoiseNCA allows creating Multiscale patterns within a single image. Notice how the scale of the patterns seamlessly changes from left to right.

Abstract

Neural Cellular Automata (NCA) is a class of Cellular Automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this paper, we focus on NCA models used for texture synthesis, where the update rule is inspired by partial differential equations (PDEs) describing reaction-diffusion systems. To train the NCA model, the spatio-termporal domain is discretized, and Euler integration is used to numerically simulate the PDE. However, whether a trained NCA truly learns the continuous dynamic described by the corresponding PDE or merely overfits the discretization used in training remains an open question. We study NCA models at the limit where space-time discretization approaches continuity. We find that existing NCA models tend to overfit the training discretization, especially in the proximity of the initial condition, also called "seed". To address this, we propose a solution that utilizes uniform noise as the initial condition. We demonstrate the effectiveness of our approach in preserving the consistency of NCA dynamics across a wide range of spatio-temporal granularities. Our improved NCA model enables two new test-time interactions by allowing continuous control over the speed of pattern formation and the scale of the synthesized patterns. We demonstrate this new NCA feature in our interactive online demo. Our work reveals that NCA models can learn continuous dynamics and opens new venues for NCA research from a dynamical systems' perspective.

BibTeX

@InProceedings{,
  title     = {NoiseNCA: Noisy Seed Improves Spatio-Temporal Continuity of Neural Cellular Automata},
  author    = {},
  booktitle = {},
  year      = {2024},
}