Fri Dec 12 09:48:54 2025

mandelbrot_area_test():
  python version: 3.10.12
  numpy version:  1.26.4
  matplotlib version: 3.5.1
  Test mandelbrot_area().

mandelbrot_area():
  Estimate the area of the Mandelbrot set.

  For  200 ^2 random values C = X + i*Y
  in the complex circle of radius 2,
  carry out up to  100  iterations of the map
  Z(n+1) = Z(n)^2 + C.
  If the iterates stay in the circle of radius 2,
  then C is a member of the Mandelbrot set.


  Iteration  0   Points escaping = 0
  Iteration  1   Points escaping = 2892
  Iteration  2   Points escaping = 9568
  Iteration  3   Points escaping = 9304
  Iteration  4   Points escaping = 3796
  Iteration  5   Points escaping = 2138
  Iteration  6   Points escaping = 1206
  Iteration  7   Points escaping = 860
  Iteration  8   Points escaping = 568
  Iteration  9   Points escaping = 460
  Iteration  10   Points escaping = 320
  Iteration  11   Points escaping = 250
  Iteration  12   Points escaping = 210
  Iteration  13   Points escaping = 166
  Iteration  14   Points escaping = 116
  Iteration  15   Points escaping = 120
  Iteration  16   Points escaping = 108
  Iteration  17   Points escaping = 82
  Iteration  18   Points escaping = 92
  Iteration  19   Points escaping = 74
  Iteration  20   Points escaping = 54
  Iteration  21   Points escaping = 44
  Iteration  22   Points escaping = 36
  Iteration  23   Points escaping = 62
  Iteration  24   Points escaping = 44
  Iteration  25   Points escaping = 32
  Iteration  26   Points escaping = 28
  Iteration  27   Points escaping = 28
  Iteration  28   Points escaping = 32
  Iteration  29   Points escaping = 42
  Iteration  30   Points escaping = 16
  Iteration  31   Points escaping = 12
  Iteration  32   Points escaping = 32
  Iteration  33   Points escaping = 10
  Iteration  34   Points escaping = 20
  Iteration  35   Points escaping = 12
  Iteration  36   Points escaping = 20
  Iteration  37   Points escaping = 24
  Iteration  38   Points escaping = 12
  Iteration  39   Points escaping = 12
  Iteration  40   Points escaping = 18
  Iteration  41   Points escaping = 18
  Iteration  42   Points escaping = 10
  Iteration  43   Points escaping = 6
  Iteration  44   Points escaping = 4
  Iteration  45   Points escaping = 10
  Iteration  46   Points escaping = 16
  Iteration  47   Points escaping = 10
  Iteration  48   Points escaping = 6
  Iteration  49   Points escaping = 8
  Iteration  50   Points escaping = 8
  Iteration  51   Points escaping = 12
  Iteration  52   Points escaping = 2
  Iteration  53   Points escaping = 8
  Iteration  54   Points escaping = 12
  Iteration  55   Points escaping = 4
  Iteration  56   Points escaping = 6
  Iteration  57   Points escaping = 2
  Iteration  58   Points escaping = 2
  Iteration  59   Points escaping = 6
  Iteration  60   Points escaping = 6
  Iteration  61   Points escaping = 2
  Iteration  62   Points escaping = 6
  Iteration  63   Points escaping = 10
  Iteration  64   Points escaping = 6
  Iteration  65   Points escaping = 4
  Iteration  66   Points escaping = 4
  Iteration  67   Points escaping = 8
  Iteration  68   Points escaping = 4
  Iteration  69   Points escaping = 0
  Iteration  70   Points escaping = 2
  Iteration  71   Points escaping = 8
  Iteration  72   Points escaping = 0
  Iteration  73   Points escaping = 8
  Iteration  74   Points escaping = 2
  Iteration  75   Points escaping = 0
  Iteration  76   Points escaping = 2
  Iteration  77   Points escaping = 2
  Iteration  78   Points escaping = 8
  Iteration  79   Points escaping = 2
  Iteration  80   Points escaping = 2
  Iteration  81   Points escaping = 0
  Iteration  82   Points escaping = 2
  Iteration  83   Points escaping = 10
  Iteration  84   Points escaping = 2
  Iteration  85   Points escaping = 4
  Iteration  86   Points escaping = 4
  Iteration  87   Points escaping = 2
  Iteration  88   Points escaping = 8
  Iteration  89   Points escaping = 2
  Iteration  90   Points escaping = 4
  Iteration  91   Points escaping = 4
  Iteration  92   Points escaping = 4
  Iteration  93   Points escaping = 0
  Iteration  94   Points escaping = 0
  Iteration  95   Points escaping = 0
  Iteration  96   Points escaping = 4
  Iteration  97   Points escaping = 0
  Iteration  98   Points escaping = 2
  Iteration  99   Points escaping = 4
  Iteration  100   Points escaping = 2
  Points still inside =  6786  out of  40000

  Estimated area =  1.52685
  Cook estimate was 1.5129
  Graphics saved as "mandelbrot_area.png"

mandelbrot_area_test()
  Normal end of execution.
Fri Dec 12 09:48:59 2025