Polynomial Regression vs NCA Memories

Polynomial Regression is your calculator and, more importantly, learning tool. You will be able to: * Construct polynomials of up to 20 degrees from either real or complex roots. * Interpolate polynomials from points by Lagrange, Newton or Vandermonde methods and Quadratic or Cubic splines. * Perform Least Squares approximation by orthogonal projection, with or without QR factorization, or partial derivatives. * Learn about each of the algorithms with derivations, proofs, step by step demonstrations, and visual tools. * Have an option to enter data by either typing or tapping on XY plane, and save data sets between program runs.

Unleash a Universe in Your Pocket Dive into the mesmerizing, complex world of cellular automata with NCA Memories! This isn't just another simulator; it's a high-performance digital laboratory powered by Apple's Metal API. We harness the full power of your device, running simulations at full native resolution to reveal a level of detail you've never seen before. Watch intricate patterns emerge, evolve, and react to your touch. Use the intuitive brush interface to paint new life onto the canvas, erase sections to see what happens, or inject chaos with a spray of noise. You are in complete control of your own digital ecosystem. Key Features: Explore Diverse Rules: Go beyond the classics. Experiment with a library of different cellular automata update rules, each creating its own unique patterns, "organisms," and behaviors. Blazing Metal Performance: Our custom Metal shader is designed for one thing: speed. Experience fluid, high-FPS simulations without compromising on resolution. Interactive Brush: Don't just watch - create! Paint, draw, and interact with the simulation in real-time. It's a dynamic canvas for digital life. Total Tunability: You're the one in charge. Update Rate: Slow things down to study every change or crank it up for high-speed evolution. Noise Parameters: Introduce random elements and watch the simulation adapt. Simulation Resolution: Run at glorious native resolution or scale it down for different effects. Target FPS: Manually set your target frame rate to balance performance and battery life. Whether you're an artist looking for a new source of inspiration, a student of complex systems, or just looking for a beautiful, interactive toy, NCA Memories is your sandbox. Download now and start creating worlds! Note: The simulation rules in this app are based on the research paper "Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata" by Ehsan Pajouheshgar, Aditya Bhardwaj, Nathaniel Selub, and Ethan Lake (arXiv:2508.15726). This app is an independent implementation inspired by their work. You can explore their original research and interactive demo at: memorynca.github.io/2D/