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Mandelbrot Set Explorer

A fully-functional Mandelbrot set explorer using Open Hexagon's new shader support.

Controls:
* Moving will zoom by default.
* Press swap to cycle between zooming, panning on the real axis (left/right), panning on the imaginary axis (up/down), changing the power and changing the number of iterations.
* Press focus to change the power back to the default of 2.

The Mandelbrot set is defined as the set of complex numbers for which iterating the function zₙ₊₁ = zₙ² + c (starting with z₀ = 0) does not diverge to infinity (these are the black regions; other colours are assigned depending on how quickly a particular complex number diverges). Generating the Mandelbrot set perfectly would require iterating this function an infinite number of times for some numbers, which is obviously impossible, so instead generators such as this will perform a certain number of iterations before giving up and assuming a number is part of the Mandelbrot set. Increasing the number of iterations will produce more detail but also decrease the framerate, especially in areas with a lot of black.
Changing the power will change the square in zₙ² + c to a different power. Non-integer and negative powers are supported, and sometimes produce some interesting results.

If you zoom in too far, the image will appear pixelated - this is simply due to limitations in the precision of floating-point numbers. (OpenGL's support for double precision floats is limited and trigonometric functions are not supported, which is required to raise a complex number to a non-integer power.)

Requires Open Hexagon 2.1.5 or later.

Music credit:
Frozen Star Kevin MacLeod ( https://incompetech.com/ )
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/