Explore the Mandelbrot Set

There are hundreds of programs for generating fractal images on your desktop computer, but there are only a few for the iPhone and iPad. The math is simple, but there’s a lot of it; you need a fast processor to do a decent job. The iPhone, iPod touch, and iPad are up to the task, but only if the application has been designed to take full advantage of the hardware resources. That’s Brot.

Brot uses numerous tricks and optimizations so its performance on the iPhone, iPod touch, and iPad is truly exceptional. No frustrating delays while waiting for the next image (instantaneous at low levels; just a few seconds at the deepest level and highest precision). Simply tap the screen to zoom in to a particular spot (or double-tap to zoom out). You can drag-scroll, then zoom again. Hit "Play" to take a ride through your sequence. The current image or your complete path (the image sequence) can be saved for recall and enjoyment at another time.

Features:
• Uses a very fast tracing algorithm.
• Automatic lookahead pre-computes the next image in the background.
• Tap: zoom in; double-tap: zoom out. (Does not use pinch.)
• Zoom in to about 50 levels (each level is an additional 2x magnification).
• Replay your path (movie-like).
• "Progressive" mode shows image generation in real time.
• Save/Restore favorite images and image sequences.
• Images can be sent to Photos (and hence Mail).
• Huge selection of color sequences.
• Three precision settings.

Independent review: http://www.1stimpressions.mobi/2010/09/20/brot/

Note: Has not been updated yet for the new iPad's retina display, but I'm working on it.