Drawing with Math vs FrankenCA

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.

Touch a living lattice and watch local rules become motion, structure, transport, and surprise. FrankenCA contains nineteen cellular-automata systems rendered through a native Metal pipeline. Move quickly between automata, run them full screen, reseed or mutate a field, and open the full lab when you want direct control over the active system. The collection spans continuous morphogenesis, transport, topology, spin systems, geometry, bifurcations, and quantum-inspired dynamics. Each automaton has its own visual language and parameter set instead of sharing a cosmetic preset. The native theory atlas explains the governing state, update rule, and important parameters with proper mathematical notation, diagrams, tables, and process views. The equations and simulations are bundled with the app and remain available offline. FrankenCA has no account, advertising, tracking, web view, or cloud computation. Simulation state and gestures stay on the device.