Fracture: fractal viewer built with HTML canvas

NOTE: This app works, but the code has become overcomplicated and difficult to build on. I am currently planning a complete overhaul of the codebase (in particular the JavaScript related to the UI). After that, I will hopefully be able to add features more easily.

Main page is located at main.html (view online).

• Displays these fractals:
  • Mandelbrot set and Julia sets
  • Multibrot sets and Julia sets
  • Burning Ship fractal and Julia sets
  • Multiship fractals and Julia sets (Burning Ships and Julia sets with an exponent other than 2)
  • Tricorn fractal and Julia sets
  • Mulicorn fractals and Julia sets
• Adjustable parameters:
  • Iterations
  • Canvas size
  • Escape radius
  • Julia constants and exponents
• Zooming:
  • Clicking (to focus on a point)
  • Drag and release (to focus on a region)
    • Press Esc to cancel a drag
• Center the image with Ctrl + click
• Use Alt + click to view a point's corresponding Juila set or to switch back to the original image
• Downloadable images
• NEW: Custom palettes
• More features and fractals coming!

Code / features todo list:

• Add more toolbar options:
  • Image quality:
    • Anti-aliasing
    • Smooth coloring
    • More color options (aka premade palettes / coloring functions)
• Add new fractals:
  • Rational maps
  • Phoenix fractal (feedback from previous iterations)
  • Newtonian fractals?
  • Collatz fractal
  • Custom fractal
    • Equation (+ parser)
    • Iteration style: Mandelbrot or Julia
    • Misc. math functions (abs, log, trig functions)
    • Feedback from previous iterations
• Prevent scientific notation for complex coordinates (especially close to im = 0)
• Add help section/popup
• Dynamically built functions to improve rendering time?
  • This can also facilitate new options such as:
    • Hybrid fractals
    • More flexible palettes
• "Touch up" function: only recalculate image if necessary (i.e. something about the fractal changed); This will allow for faster palette manipulation to fine-tune a render.
• Friendly palette UI (instead of text)
• Streamline toolbar structure
• Shorten variable and function names

Samples: