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. ; ; 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 }