NCA Memories vs Surface Explorer

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/

Surface Explorer is a high-performance visualizer for intricate mathematical surfaces — 2D manifolds embedded in three- or four-dimensional space, and 3D slices of four-dimensional hypersurfaces — bringing abstract geometry to life with real-time GPU rendering. KEY FEATURES • Cross Section — slice four-dimensional hypersurfaces and watch their 3D sections change shape as you rotate them in 4D or slide the cutting plane along the fourth axis, even along a 4D camera path. • Ray Marching Engine — real-time rendering of implicit surfaces and signed-distance fields, with procedural displacement, transparency, adjustable shells, and a precise mode for high-degree equations. • Multi-Mesh Surfaces — build figures from several independent grids, set with a single field or a script, each with its own color, transparency, texture, image and domain. • Solid Curve — write a curve in 3D or 4D and see the tube drawn around it, with adjustable thickness; several tubes from a script. • Surface Borders — add a tube along the edges of a parametric surface, with its own color, texture and thickness. • Geodesic Flow — explore intrinsic geometry on curved manifolds (S³, H²×R, SL(2,R) and more), integrating geodesics from initial conditions. • 4D Spatial Exploration — dedicated controls for hyperspatial rotation (Omega, Phi, Psi), projection, and 3D and 4D camera paths. • 4D Lighting Models — Directional, Observer, and Slice lighting designed for hyperspace. • Dynamic GLSL Scripting — write custom shaders for procedural textures and surface logic in the built-in editor. • Backgrounds — images and procedural effects, fixed on screen or wrapped around the scene as a sphere, cylinder or cube. • Audio-Visual Synthesis — synchronize geometric parameters with a mathematical sound synthesizer. • Video Recording — capture your explorations directly in the app and save them to your device. A library of ready-made presets ships with the app, from classic parametric surfaces to black-hole ergospheres, curved-space tori and slices of the 3-torus, together with a searchable built-in manual. Built with Qt and Metal for smooth, native performance on iPhone and iPad.