extensions [ gis matrix ] globals [divisions fractal-dim len walk-count old-box-count new-box-count x-axis-list y-axis-list box-size explore? iteration iterations-to-go slope lin-reg-eq any-new-boxes? r-square automatic-bcd? ] breed ;used only for taking box counting dimension of fractal examples. [boxes box] boxes-own [past? present? future?] patches-own [fractal?] ;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;import image;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;; to setup clear-all if image = "coastline" [ import-pcolors "Coastline.png" ask patches with [pcolor != white] [set pcolor black] ] if image = "tree" [ import-pcolors "Tree.png" ask patches with [pcolor != white] [set pcolor black] ] if image = "custom-image" [ import-pcolors "custom-image.png" ;make sure your image is a square with colors that represent what you're interested in dimensioning (black and white is easiest) ] set explore? false set automatic-bcd? true set x-axis-list [ ] set y-axis-list [ ] ask turtles [die] set box-size initial-box-length set iteration 0 reset-ticks end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;Box-Counting-Dim;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to bcd-go set len initial-box-length bcd-begin end to bcd-begin ask boxes ; clears screen in case there are any old boxes [die] if automatic-bcd? [ if box-size >= initial-box-length [ set automatic-bcd? false] ] if ticks != 0 [set box-size box-size + increment set iteration iteration + 1 set iterations-to-go 91 - iteration ] set old-box-count 0 set new-box-count 1 ;eliminates an error for first round make-initial-box make-neighbors-count-patches end to setup-bcd set box-size initial-box-length make-initial-box end ;makes a starter box at the beginning of each run with present? = true. ;This box will then be used to make boxes with future? = true ;which will be used for the next run. to make-initial-box create-boxes 1 ask boxes [ set shape "square" set size box-size setxy -60 0 set heading 90 set color red set past? false set present? true set future? false ] end ;makes a Moore neighborhood around the starter box and counts patches below each new box (exploit). ;If there are no new boxes with patches under them for a given run a box is sent outside the neighborhhod ;to cover non-contiguous patches (explore). If this box finds no new patches the run is complete. to make-neighbors-count-patches ask boxes with [present? = true ] [make-neighbors] ask boxes with [future? = true] [exploit] count-new-boxes if any-new-boxes? = false [explore] if any-new-boxes? = false [calculate-box-counting-dimension] if any-new-boxes? = false and automatic-bcd? [ bcd-begin stop ] update-past-present-future-states tick if any-new-boxes? = true [make-neighbors-count-patches] end to make-neighbors hatch 1 [fd box-size rt 90 set present? false set future? true hatch 1 [fd box-size rt 90 set present? false set future? true hatch 1 [fd box-size set present? false set future? true hatch 1 [fd box-size rt 90 set present? false set future? true hatch 1 [fd box-size set present? false set future? true hatch 1 [fd box-size rt 90 set present? false set future? true hatch 1 [fd box-size set present? false set future? true hatch 1 [fd box-size set present? false set future? true ]]]]]]]] end to exploit if count boxes in-radius (box-size / 2) > 1 ; eliminates duplicates [die] if count patches-under-me = 0 [ die ] end to-report patches-under-me report patches in-radius ( (1.4 * size ) / 2 ) with [pcolor = color-value] ; [let my-n-edge ycor + (0.5 * size) ;; if my shape is a square ; let my-s-edge ycor - (0.5 * size) ; let my-w-edge xcor - (0.5 * size) ; let my-e-edge xcor + (0.5 * size) ; report patches with [pcolor = green and ; (pycor - 0.5 < my-n-edge) and (pycor + 0.5 > my-s-edge) and ; (pxcor + 0.5 > my-w-edge) and (pxcor - 0.5 < my-e-edge) ; ] ; ] end to explore if count boxes with [present? = true] > 0 [ ask patches with [pcolor = color-value] [ ifelse count boxes in-radius ( box-size ) = 0 [set explore? true] [stop] ] ] if explore? [ ask one-of boxes with [present? = true] [ hatch 1 [ set present? false set future? true move-to min-one-of patches with [pcolor = color-value and count boxes in-radius ( box-size ) = 0 ] [distance myself]] ] ] count-new-boxes set explore? false end to count-new-boxes set old-box-count new-box-count set new-box-count count boxes ifelse old-box-count = new-box-count [set any-new-boxes? false] [set any-new-boxes? true] end to update-past-present-future-states ask boxes [ if present? = true [set past? true set present? false] if future? = true [set future? false set present? true] ] end to calculate-box-counting-dimension if count boxes >= 1 [ ; eliminates potential error message if setup is pressed during a box-counting procedure set-current-plot "Box Counting Plot" set-current-plot-pen "default" let no-boxes log (count boxes ) 10 let scale (log ( 1 / box-size ) 10 ) plotxy scale no-boxes set x-axis-list lput scale x-axis-list set y-axis-list lput no-boxes y-axis-list ] stop end to fractal-dimension if ticks = 0 [ if divisions > 0 [ ; eliminates potential error message let line-segments count turtles set fractal-dim precision(( log line-segments 10 / log divisions 10 ))3 show line-segments show divisions show fractal-dim ] ] stop end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;Linear Reg;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;Linear regression is used to find the 'best-fit' line ;through all the tuples (box-size,number of boxes) plotted in the "Number of Boxes vs. Scale" plot. ;The slope of the line is the box counting dimension. to linear-regression if count boxes >= 1 [ ; eliminates potential error message if setup is pressed during a box-counting procedure [ let regression matrix:regress matrix:from-column-list (list y-axis-list x-axis-list) ;using the regression tool from the matrix extension ;setting y-intercept and slope (measure of goodness of fit) let y-intercept item 0 (item 0 regression) set slope item 1 (item 0 regression) set r-square item 0 (item 1 regression) ; set the equation to the appropriate string set lin-reg-eq (word (precision slope 3) " * x + " (precision y-intercept 3)) set-current-plot "Box Counting Plot" set-current-plot-pen "pen-4" plot-pen-reset auto-plot-off plotxy plot-x-min (plot-x-min * slope + y-intercept) plot-pen-down plotxy plot-x-max (plot-x-max * slope + y-intercept) plot-pen-up ] end @#$#@#$#@ GRAPHICS-WINDOW 259 10 778 550 250 250 1.016 1 10 1 1 1 0 0 0 1 -250 250 -250 250 1 1 1 ticks 30.0 BUTTON 13 265 215 301 Image Setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 783 54 1050 309 Box Counting Plot log [1 / box length] log [number of boxes] -2.0 -1.0 0.0 2.0 true false "" "" PENS "default" 1.0 2 -16777216 true "" "" "pen-4" 1.0 0 -2674135 true "" "" BUTTON 125 348 251 381 Box Counting: Go BCD-go T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 782 352 1049 386 Linear Regression linear-regression NIL 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 783 308 904 353 Box-Counting Dim. slope 7 1 11 MONITOR 86 477 169 522 Box Length box-size 17 1 11 MONITOR 6 477 88 522 Iteration iteration 17 1 11 MONITOR 904 308 1016 353 Equation of Line lin-reg-eq 17 1 11 TEXTBOX 785 395 1055 428 NIL 11 0.0 1 SLIDER 8 153 207 186 color-value color-value 0 139 0 1 1 NIL HORIZONTAL TEXTBOX 9 191 260 268 Only one color value in the image can be selected for box counting. E.g., if color-value is 0, only black patches are included in box counting. Use \"Color Swatches\" under the \"Tools\" menu to see color values. 11 0.0 1 TEXTBOX 11 10 308 32 Applied Box-Counting 18 95.0 1 TEXTBOX 10 324 213 346 Box Counting Controls 16 0.0 1 CHOOSER 9 104 208 149 image image "coastline" "tree" "custom-image" 0 MONITOR 166 477 248 522 # of boxes count boxes with [color = red] 17 1 11 MONITOR 1000 308 1050 353 R^2 r-square 5 1 11 TEXTBOX 11 48 161 68 Image Examples 16 0.0 1 BUTTON 7 348 126 381 Box Counting: Setup setup-bcd NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 6 411 251 444 increment increment 0 2 1 0.1 1 NIL HORIZONTAL SLIDER 6 380 251 413 initial-box-length initial-box-length 1 10 1 1 1 NIL HORIZONTAL TEXTBOX 784 20 980 42 Box-Counting Plot 16 0.0 1 TEXTBOX 12 447 223 489 Amount that box length increases per iteration of box counting 11 0.0 1 TEXTBOX 11 73 229 115 See Info tab for instructions on how to input your own image. 11 0.0 1 @#$#@#$#@ ## WHAT IS IT? Applied Box-Counting is a model that illustrates how the box-counting method can be applied to any two-dimensional, one-color image. An image can be imported into NetLogo as a .png file. ## HOW IT WORKS See BoxCountingDimension.nlogo in the Fractals series for information on the box-counting method. ## HOW TO USE IT In the upper left hand corner of the interface, select an image example, and press "Image Setup." For example, if you select "coastline", an image of the coast of Britain should appear in the view. Only one color value in the image can be selected for box counting. E.g., if color-value is 0, only black patches are included in box counting. Use "Color Swatches" under the "Tools" menu to see color values. In the coastline example, since the coastline is black in this image, the color value should be black (color-value = 0). Press "Box Counting: Setup" and then "Box Counting: Go". A box-counting run will begin. For each iteration, boxes cover the chosen color, and the system plots the log of the number of boxes, N, versus the log of the scale, 1/r, in the plot one the right side of the interface. The model will continue iterating until you press "Box Counting: Go" again to stop the process (or 'Halt' under "Tools" in the menu bar). Press "Linear Regression" under the plot on the left side of the interface to determine the box-counting-dimension of the image. To run this model more quickly, increase the speed slider at the top of the interface to its maximum value. ## Uploading Images You can use your own images in this model. Your image file needs to be in .png format, have square dimension, and be called "custom-image.png". You also need to identify the color of the pixels that you want box-counting to measure, and find the corresponding color value from the Netlogo Color Swatches in the Tools menu. The easiest way to do this is to make the color of interest black, and set color-value to 0. Make sure that the image is square and has no black borders; the only black in the image should be part of the figure itself. Note that the larger the image, the longer it will take to run Image Setup. ## CREDITS AND REFERENCES This model is part of the Fractals series of the Complexity Explorer project. Main Author: John Driscoll Contributions from: Vicki Niu, Melanie Mitchell ## HOW TO CITE If you use this model, please cite it as: Applied Box Counting model, Complexity Explorer project, http://complexityexplorer.org ## COPYRIGHT AND LICENSE Copyright 2016 Santa Fe Institute. This model is licensed by the Creative Commons Attribution-NonCommercial-ShareAlike International (http://creativecommons.org/licenses/). This states that you may copy, distribute, and transmit the work under the condition that you give attribution to ComplexityExplorer.org, and your use is for non-commercial purposes. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line 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