I had really wanted to make it so that a user of my HTML5 Fractal software can specify an iterating function using familiar notation. This new version 2.0 makes that wish a reality. At the moment, there are limited functions that can be used in the iterating function, such as sin, cos, conj, and abs. Furthermore, exponents must be whole numbers (no fractions or imaginary exponents). I plan to overcome these limitations in a future version.
In order to draw a fractal using a custom iterating function, simply change the fractal selection to "Custom" and the interface to input the iterating function will appear. Try modifying the functions for the built-in fractals.