This paper presents a rotation-invariant embedded platform for simulating (neural) cellular automata (NCA) in modular robotic systems. Inspired by previous work on physical NCA, we introduce key innovations that overcome limitations in prior hardware designs. Our platform features a symmetric, modular structure, enabling seamless connections between cells regardless of orientation. Additionally, each cell is battery-powered, allowing it to operate independently and retain its state even when disconnected from the collective. To demonstrate the platform's applicability, we present a novel rotation-invariant NCA model for isotropic shape classification. The proposed system provides a robust foundation for exploring the physical realization of NCA, with potential applications in distributed robotic systems and self-organizing structures.

When working with tabular data, missingness is always one of the most painful problems. Throughout many years, researchers have continuously explored better and better ways to impute missing data. Recently, with the rapid development evolution in machine learning and deep learning, there is a new trend of leveraging generative models to solve the imputation task. While the imputing version of famous models such as V ariational Autoencoders or Generative Adversarial Networks were investigated, prior work has overlooked Neural Cellular Automata (NCA), a powerful computational model. In this paper, we propose a novel imputation method that is inspired by NCA. We show that, with some appropriate adaptations, an NCA-based model is able to address the missing data imputation problem. We also provide several experiments to evidence that our model outperforms state-of-the-art methods in terms of imputation error and post-imputation performance. Introduction There is no doubt that data plays a crucial role in this modern world. In numerous business and scientific applications, data is the foundation for decision-making process, enabling experts to detect noticeable patterns and take advantage of them. One of the most common types of data is tabular data, which presents in almost every domains from economics, finance to healthcare, demography. Being organized in structured rows and columns, one can straightforwardly apply statistical methods, perform calculations and draw meaningful insights from this data. Moreover, many machine learning algorithms, especially those used in supervised learning tasks, are designed to work optimally on tabular data.

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-temporal 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 system's perspective.

Neural Cellular Automata (NCA) models have shown remarkable capacity for pattern formation and complex global behaviors stemming from local coordination. However, in the original implementation of NCA, cells are incapable of adjusting their own orientation, and it is the responsibility of the model designer to orient them externally. A recent isotropic variant of NCA (Growing Isotropic Neural Cellular Automata) makes the model orientation-independent - cells can no longer tell up from down, nor left from right - by removing its dependency on perceiving the gradient of spatial states in its neighborhood. In this work, we revisit NCA with a different approach: we make each cell responsible for its own orientation by allowing it to "turn" as determined by an adjustable internal state. The resulting Steerable NCA contains cells of varying orientation embedded in the same pattern. We observe how, while Isotropic NCA are orientation-agnostic, Steerable NCA have chirality: they have a predetermined left-right symmetry. We therefore show that we can train Steerable NCA in similar but simpler ways than their Isotropic variant by: (1) breaking symmetries using only two seeds, or (2) introducing a rotation-invariant training objective and relying on asynchronous cell updates to break the up-down symmetry of the system.

As AI art generators take the world by storm, some people wonder if it should count as art at all. The technology is still evolving and has some wrinkles to iron out, which means there are indeed flaws to consider alongside the incredible artwork a good artificial intelligence can produce. Let's explore the issue by breaking down the definition of art and whether or not AI-based work fits within that umbrella. Starting with the etymology of the word, Merriam-Webster's definition states that "art" stems from the Latin word "ars", which means, among other things, acquired skill, craftsmanship, and artistic achievement. Today, there's little consensus between philosophers and artists as to what real art is.

Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable optimization method for learning the RD system parameters to perform example-based texture synthesis on a 2D plane. We do this by representing the RD system as a variant of Neural Cellular Automata and using task-specific differentiable loss functions. RD systems generated by our method exhibit robust, non-trivial 'life-like' behavior.

Early in the morning on May 18, 2015, Alexander Mordvintsev made an amazing discovery. He had been having trouble sleeping. Just after midnight, he awoke with a start. He was sure he'd heard a noise in the Zurich apartment where he lived with his wife and child. Afraid that he hadn't locked the door to the terrace, he ran out of the bedroom to check if there was an intruder. All was fine; the terrace door was locked, and there was no intruder.

Go grandmaster Lee Sedol recently announced he was retiring from the game because "there is an entity that can never be defeated": AI. As readers likely remember, an artificial intelligence known as AlphaGo defeated Lee in 2016. The grandmaster later commented that AlphaGo had displayed "human intuition." AI is in the news regularly these days, but one area is still hugely underreported: its potential to be creative. Machines such as AlphaGo are unquestionably displaying clear glimmerings of creativity.