Curved Spaces vs Mandel Draw

Curved Spacess is a flight simulator for multi-connected universes. Because light itself wraps around such a space, inhabitants see their universe’s contents repeating in a crystalline pattern, like a hall of mirrors but with no reflection. Curved Spaces is intended for undergraduates and graduate students studying 3‑manifolds, and has also found use as a research tool in topology and cosmology. Recreational math enthusiasts may instead prefer Torus Games, which offers 3D Mazes and 3D Tic-Tac-Toe in a variety of multi-connected 3D spaces, along with games on multi-connected 2D surfaces.

Mandel Draw is an application that allows you to enjoy fractals, Mandelbrot sets and filled Julia sets, in a fast and comfortable way. The app allows you to draw an infinite number of fractal images from up to 80 different functions, 20+α color palettes, and freely configurable Julia parameters. Operation is simple. Drag to move, pinch to zoom in and out. Double- and triple-tap operations are also available. Convenient settings are also available. - Use DF64 operation: Double the float operation to make it possible to zoom in more. (Disabled in the Appendix 1,2) - Select render version: Two types of rendering methods can be selected. - Display coordinates and magnification: The current coordinates and magnification will be displayed on the screen. - Output detailed information: Add detailed information to the text when sharing. - High-resolution output: Outputs at 4 times the vertical and horizontal resolution when sharing. - iCloud Sync: Share favorites and My Palette with another iPhone or iPad. In addition, all functions are available when unlocked with in-app purchase. 1) All functions are selectable 2) All palettes can be selected 3) Up to 2000 favorites can be saved 4) Maximum number of My Palettes that can be saved is now 30. Now, please enjoy the wonderful and mysterious world of fractals. What is a fractal? Simply put, a fractal is a self-similar figure that does not lose its complexity no matter how much it is enlarged. (Though computers have their limitations.) There are various fractal shapes, such as the Koch curve, Sierpinski's gasket, and Menger's sponge. The Mandelbrot set and the filled Julia set are fractals drawn computationally on the complex plane.