We will be sampling the Mandelbrot set in a rectangular grid and rendering each point as a square pixel. Doing this requires making some decisions.
- how many pixels? N::Int -> 1000x1000
- location, scale, and orientation? (center::Complex, middle_left::Complex)
- max number of iterations? maxiter::Int -> unknown function of unknown variables. "distance from the set" with "the right" metric
- stop condition? stop()::Function{Complex -> boolean}
- color? color()::Function{IteratorState -> RGB}
Some recipes for generating pictures
- External rays (vector)
- Parameter
- Angle
- Radius of 'infinity'
- Segment resolution
- Depth
- Colors
- External Binary decomposition (raster)
- Parameter
- Grid size
- Grid location
- Radius of 'infinity'
- Angle of decomposition
- Max iter ~ depth
- Colors
- Escape Time (raster)
- Parameter
- Grid size
- Grid location
- Max iter ~ depth
- Escape radius ~ radius of 'infinity'
- Colors
- Inverse Iterate (vector)
- Parameter
- Start point
- Number of generations
-question: should all generations be plotted? or just the last? does it matter?
Combos
From angle: Boundary of the Julia set with inverse iterates
Hubbard tree inside
External rays outside
From angle: Binary decomp outside
Binary decomp inside