PythagorasTree vs Mandelbrot Flight Simulator

The Pythagoras Tree is math art. A square trunk is drawn. The hypotenuse of a right triangle is laid on top of the square. From the two legs two new squares are drawn. This process is repeated recursively until there the size of the square is too small to draw. Here you can adjust the angles of the triangle and the color of the tree. You can also make the tree grow and shrink to see the steps in making the tree.

Navigate an infinite mathematical universe in real time. Mandelbrot Flight Simulator renders the legendary Mandelbrot set directly on your device's GPU. Pinch to zoom into breathtaking fractal detail, drag to explore, and watch the companion Julia set update live as you move through the plane. Every point in the Mandelbrot set corresponds to a unique Julia set — an infinite catalog of alien geometry, generated from the simplest possible rule. This app lets you browse that catalog in real time. WARNING: YOUR MIND WILL BE BLOWN! FEATURES • Watch the Julia set morph in real time as you drag around the Mandelbrot set • Turn on Autopilot mode to watch preprogrammed flythroughs • GPU-accelerated rendering at up to 60 fps • Five view modes including split-screen and dedicated full-screen Mandelbrot and Julia views • Multiple spectacular color schemes • Pinch to zoom, drag to pan, long-press to zoom continuously • Save stunning fractal screenshots to your photo library TIPS • Tap anywhere onscreen to open the menu. • Turn on autopilot mode to let the app take you on a tour • Zoom in to discover infinite fractal detail. • Hunt for the most intricate and beautiful Julia sets at the chaotic border of the Mandelbrot set. WHAT YOU'RE SEEING The Mandelbrot set is the collection of all points in the complex plane whose orbits stay bounded under the iteration z → z² + c. Its boundary is infinitely complex — zoom in anywhere and new structure always emerges. The colors show how quickly nearby points escape to infinity. The Julia set is a companion fractal. For any point you pick in the Mandelbrot set, there exists a unique Julia set with that point as its parameter. Points deep inside the Mandelbrot set produce solid, connected Julia sets. Points near the boundary produce intricate, fragmented ones. This app makes that relationship tangible and explorable. INSPIRATIONS Ben Sparks Holly Krieger Damnimp Tom Kerrigan Benoit B. Mandelbrot Gaston Julia