# Chaos Fractal Toolkit

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### VERSION

$Id: Chaos Fractal Toolkit.nlogo 39714 2008-05-01 18:14:18Z tisue $

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### NETLOGO FEATURES

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## Comments and Questions

breed [ squares square ] breed [ outlines outline ] breed [ points point ] squares-own [ my-size half-size my-rotation-angle reflection-matrix rotation-matrix scale-matrix xadjustment yadjustment ] globals [ function-list ] to setup ca set-default-shape squares "square 4" set-default-shape outlines "square 3" set function-list [] create-outlines 1 [ setxy .5 .5 set size 1.44 ] create-points 100 [ setxy 0 0 set size .010001 ] end to iterate-sierpinski let random-function random 3 if( random-function = 0 ) [ setxy ( .5 * xcor ) + ( 1 / 2 ) ( .5 * ycor ) + ( 0 ) ] if( random-function = 1 ) [ setxy ( .5 * xcor ) + ( 0 ) ( .5 * ycor ) + ( 0 ) ] if( random-function = 2 ) [ setxy ( .5 * xcor ) + ( 1 / 4 ) ( .5 * ycor ) + ( sqrt(3) / 4 ) ] end to iterate-quint let random-function random 5 if( random-function = 0 ) [ setxy ( ( 1 / 3 ) * xcor ) + ( 0 ) ( ( 1 / 3 ) * ycor ) + ( 0 ) ] if( random-function = 1 ) [ setxy ( ( 1 / 3 ) * xcor ) + ( 2 / 3 ) ( ( 1 / 3 ) * ycor ) + ( 0 ) ] if( random-function = 2 ) [ setxy ( ( 1 / 3 ) * xcor ) + ( 1 / 3 ) ( ( 1 / 3 ) * ycor ) + ( 1 / 3 ) ] if( random-function = 3 ) [ setxy ( ( 1 / 3 ) * xcor ) + ( 0 ) ( ( 1 / 3 ) * ycor ) + ( 2 / 3 ) ] if( random-function = 4 ) [ setxy ( ( 1 / 3 ) * xcor ) + ( 2 / 3 ) ( ( 1 / 3 ) * ycor ) + ( 2 / 3 ) ] end to iterate-leaves let random-function random 7 if( random-function = 0 ) [ setxy ( ( 1 / 3 ) * x ) + ( 2 / 3 ) ( ( 1 / 3 ) * ycor ) + ( 0 ) ] if( random-function > 0 and random-function < 3 ) [ ;setxy ( ( sqrt(2) / 2 ) * ( sqrt(2) / 3 ) * xcor - ( sqrt(2) / 2 ) * ( sqrt(2) / 3 ) * ycor ) + ( 1 / 3 ) ; ( ( sqrt(2) / 2 ) * ( sqrt(2) / 3 ) * xcor + ( sqrt(2) / 2 ) * ( sqrt(2) / 3 ) * ycor ) + ( 0 ) setxy ( ( 2 / 6 ) * xcor - ( 2 / 6 ) * ycor + ( 1 / 3 ) ) ( ( 2 / 6 ) * xcor + ( 2 / 6 ) * ycor + 0 ) ] if( random-function > 2 and random-function < 7 ) [ setxy ( ( 2 / 3 ) * xcor ) + ( 1 / 3 ) ( ( 2 / 3 ) * ycor ) + ( 1 / 3 ) ] end to iterate-problem-a let random-function random 11 if( random-function >= 0 and random-function < 4 ) [ ;; lower left box setxy ( ( 1 / 2 ) * xcor ) + ( 0 ) ( ( 1 / 2 ) * ycor ) + ( 0 ) ] if( random-function >= 4 and random-function < 8 ) [ ;; upper right rotated box setxy ( - ( 1 / 2 ) * ycor ) + ( 1 ) ( ( 1 / 2 ) * xcor ) + ( 1 / 2 ) ] if( random-function = 8 ) [ setxy ( ( 1 / 4 ) * xcor ) + ( 1 / 2 ) ( ( 1 / 4 ) * ycor ) + ( 0 ) ] if( random-function = 9 ) [ setxy ( ( 1 / 4 ) * xcor ) + ( 3 / 4 ) ( ( 1 / 4 ) * ycor ) + ( 0 ) ] if( random-function = 10 ) [ setxy ( - ( 1 / 4 ) * ycor ) + ( 1 ) ( ( 1 / 4 ) * xcor ) + ( 1 / 4 ) ] end to iterate-problem-b let random-function random 3 if( random-function = 0 ) [ ;; large box setxy ( - ( 1 / 2 ) * ycor ) + ( 1 / 2 ) ( ( 1 / 2 ) * xcor ) + ( 1 / 2 ) ] if( random-function = 1 ) [ setxy ( ( 1 / 2 ) * xcor ) + ( 0 ) ( ( 1 / 2 ) * ycor ) + ( 0 ) ] if( random-function = 2 ) [ setxy ( ( 1 / 2 ) * xcor ) + ( 1 / 2 ) ( ( 1 / 2 ) * ycor ) + ( 0 ) ] end to-report x report xcor end to move-squares if mouse-down? [ let candidate min-one-of squares [distancexy mouse-xcor mouse-ycor] if [distancexy mouse-xcor mouse-ycor] of candidate < 1 [ ask candidate [ set color red ] while [mouse-down?] [ ;; If we don't force the display to update, the user won't ;; be able to see the turtle moving around. display ;; The SUBJECT primitive reports the turtle being watched. ask candidate [ setxy mouse-xcor mouse-ycor ] ] ask candidate [ set color white ] ask candidate [ check-bounds ] stop ] ] end to check-bounds ;; square procedure if( ( xcor - half-size ) < 0 ) [ set xcor half-size ] if( ( xcor + half-size ) > 1 ) [ set xcor 1 - half-size ] if( ( ycor - half-size ) < 0 ) [ set ycor half-size ] if( ( ycor + half-size ) > 1 ) [ set ycor 1 - half-size ] end to delete-squares if( mouse-down? and any?( squares ) ) [ let candidate min-one-of squares [distancexy mouse-xcor mouse-ycor] if [distancexy mouse-xcor mouse-ycor] of candidate < 1 [ ask candidate [ die ] stop ] ] end to create-fractal ;; point procedure if( function-list = [] ) [ set function-list ifs-list ] let random-function random-float 1 let counter 0 let right-function [] while [ counter < length function-list ] [ if( random-function < item 0 ( item counter function-list ) ) [ set right-function item counter function-list ] set counter counter + 1 ] reflect-point ( item 1 right-function ) rotate-point ( item 2 right-function ) scale-point ( item 3 right-function ) ;; moves from original square position set xcor xcor + item 4 right-function set ycor ycor + item 5 right-function ; set xcor ( item 1 right-function * xcor ) + ( item 2 right-function * ycor ) + ( item 5 right-function ) ; set ycor ( item 3 right-function * xcor ) + ( item 4 right-function * ycor ) + ( item 6 right-function ) end to reflect-point [ my-reflection-matrix ] ;; this reflects and resets inside original square set xcor ( item 0 my-reflection-matrix * xcor ) + ( item 1 my-reflection-matrix * ycor ) + item 4 my-reflection-matrix set ycor ( item 2 my-reflection-matrix * xcor ) + ( item 3 my-reflection-matrix * ycor ) + item 5 my-reflection-matrix end to rotate-point [ my-rotation-matrix ] set xcor ( item 0 my-rotation-matrix * xcor ) + ( item 1 my-rotation-matrix * ycor ) + item 4 my-rotation-matrix set ycor ( item 2 my-rotation-matrix * xcor ) + ( item 3 my-rotation-matrix * ycor ) + item 5 my-rotation-matrix end to scale-point [ my-scale-matrix ] ;; scales down original square area set xcor ( item 0 my-scale-matrix * xcor ) + ( item 1 my-scale-matrix * ycor ) set ycor ( item 2 my-scale-matrix * xcor ) + ( item 3 my-scale-matrix * ycor ) end to-report ifs-list let iterated-function-list [] ;; list of lists let total-area-of-squares ( sum [ my-size ] of squares ) let prob-counter 1 ask squares [ ;; scale, then reflect, then correct ; let entry-a ( item 0 scale-matrix * item 0 reflection-matrix ) + ( item 2 scale-matrix * item 1 reflection-matrix ) ; let entry-b ( item 1 scale-matrix * item 0 reflection-matrix ) + ( item 3 scale-matrix * item 1 reflection-matrix ) ; let entry-c ( item 0 scale-matrix * item 2 reflection-matrix ) + ( item 2 scale-matrix * item 3 reflection-matrix ) ; let entry-d ( item 1 scale-matrix * item 2 reflection-matrix ) + ( item 3 scale-matrix * item 3 reflection-matrix ) ;;set half-size my-size / 2 ;; list elements: probability determined by ratio of area, ;; rotation matrix a b c d ;; x ( my xcor - half my size ) ;; y ( my ycor - half my size ) set iterated-function-list lput ( list ( prob-counter ) reflection-matrix rotation-matrix scale-matrix ( xcor - half-size ) ( ycor - half-size ) ) iterated-function-list ;;item 0 : prob counter ;;item 1 : reflection matrix ;;item 2 : rotation matrix ;;item 3 : scale matrix ;;item 4 : xcor of bottom left corner ;;item 5 : ycor of bottom left corner set prob-counter ( prob-counter - ( my-size / total-area-of-squares ) ) ] report iterated-function-list end

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