Fortuitous Mistakes {
; By Adam Schwalbe (please email me with comments/bugs/fixes)
; aschwalbe@alaska.com
;
; (Warning! Still a work in progress, Read: buggy)
; (Also, be patient with this one, lotsa pre-loop calcs.)
; I stumbled upon this 'fractal' quite by acident.
; I was writing the code for another formula I hope to post soon,
; and I did the Algebra incorrectly.  The results I find quite pleasing :-)
; 
; The formula takes an equation and recalculates the x and y coordinates 
; and stores the results in an array (If the coordinates are within the 
; viewing area.)
;
; It then calculates the distance to the closest calculated point
; for each point stored in the array, and uses that information, 
; to scale the size of each "point" as it is displayed.  
;
; A nice #magn value is 0.3 (Just be prepared, will take a bit)
;
; Bugs: 
; 1)  You can zoom in and out only by changing the magnification.
; If you pan left or right or rotate, things break.
; (I hope to have this one fixed within a day or so.)
; 2)  I could really use some help with this one.  
; Maxiter controls the number of colours/shades for each point.
; If the #maxiter value is raised above 15 black areas appear.
; I really want to be able to add more colour to this one so any 
; help from you coders out there would be greatly appreciated.
; Hope you enjoy this one.  Adam.
 

global:

  int i
  int j
  int steps
  float y
  float x
  float y1
  float x1
  float x2 
  float y2
  float x3
  float y3
  float regraphx[round((@intervale-@intervals)/@step)+1]
  float regraphy[round((@intervale-@intervals)/@step)+1]
  float mindistance[round((@intervale-@intervals)/@step)+1]
  float distance

  i = 0
  
  ; This portion recalculates the x,y cooridinates for y = 200*x
  ; for interval given in the parameters. And stores the new values in
  ; an array if they are within the viewing area.
  ;
  x=@intervals
  repeat
      y = 200*x
      if tan(x) != tan(y)
        y1 = ((tan(x)*x)+(tan(y)*x))/2
        x1 = (2 * y1) / (tan(x) + tan(y))
        if x1 < (2/#magn) && x1 > (-2/#magn) && y1 < (1.5/#magn)&& y1 > (-1.5/#magn) 
          regraphx[i] = x1
          regraphy[i] = y1
          i = i + 1
        endif
      endif
      x = x + @step
  until x >= @intervale
  steps = i  
  
  i = 0
  j = 0
  
  ; This portion calculates the distance to the nearest recalculated points 
  ; stored in the above arrays.  It stores the value in a new array to be
  ; used in calculating the size of the new 'points' when they are displayed
  ; during the 'loop:' portion.
  ;
  repeat
    x3 = regraphx[j]
    y3 = regraphy[j]
    mindistance[j] = 1000
    repeat
      x2 = regraphx[i]
      y2 = regraphy[i]
      i = i + 1
      distance = sqrt ((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2))
      if mindistance[j] > distance && distance != 0
        mindistance[j] = distance
      endif  
    until i >= steps
    j = j + 1
    i = 0
  until j >= steps

init:
  bool bail = false
  int maxcoloriter
  int coloriter = 0
  z = #pixel
  float dist
  float x4 = real(z)
  float y4 = imag(z)
  float x5
  float y5
  int k = 0
  int l = 0
  float mindist = 1000
  
  ; This portion calculates the distance from the current pixel to the nearest
  ; 'point' stored in the array.  If the distance is less than the distance to 
  ; the nearest point stored in the array above, the pixel is shaded accoring 
  ; to the ratio of #maxiter to the distance from the current pixel to nearest
  ; point.
  ; 
  ; Bug:  If #maxiter is greater than 15 I get strange results.  I can't figure 
  ; it out.  Any help would be greatly appreciated.
  ;
  repeat
      x5 = regraphx[k]
      y5 = regraphy[k]
      dist = sqrt ((x5-x4)*(x5-x4) + (y5-y4)*(y5-y4))
      if mindist > dist
        mindist = dist
        l = k
      endif
      k = k + 1  
  until k >= steps
  if mindist <= mindistance[l] 
    maxcoloriter = #maxiter - round(((mindist/mindistance[l]) * #maxiter)+1) 
  else
    maxcoloriter = 0
  endif
  
  coloriter = 0
  ;if mindist < sqrt(((2/#magn)/#width)^2 + ((1.5/#magn)/#height)^2)
  ;  maxcoloriter = 4
  ;else 
  ;  maxcoloriter = 0
  ;endif  
  
loop:

  if maxcoloriter <= coloriter
    bail = true
  endif
  coloriter = coloriter +1
    
bailout:
  bail == false
  
default:
  title = "Fortuitous Mistakes"
  helpfile = "adam-help/FM.htm"
  center = (0,0)
  method = onepass
  magn = 0.6
  maxiter = 15
    
  param @intervals
    caption = "X start"
    default = -200
  endparam
  
  param @intervale
    caption = "X end"
    default = 200
  endparam
  
  param @step
    caption = "Step for X"
    default = .001
  endparam
}