'# Mandelbrot Set

import complex
import plot

# Escape time algorithm

def update(c:Complex, z:Complex) -> Complex = c + (z * z)

tol = 2.0
def inBounds(z:Complex) -> Bool = complex_abs(z) < tol

def escapeTime(c:Complex) -> Nat =
  z <- with_state(zero :: Complex)
  bounded_iter(1000, 1000) \i.
    case inBounds(get(z)) of
      False -> Done(i)
      True ->
        z := update(c, get(z))
        Continue

# Evaluate on a grid and plot the results

xs = linspace(Fin 300, -2.0, 1.0)
ys = linspace(Fin 200, -1.0, 1.0)

escapeGrid = each(ys) \y. each xs \x. n_to_f(escapeTime(Complex(x, y)))

:html matshow(-escapeGrid)
> <html output>