globals[previous-intensity] patches-own [ day? ;; indicates if the cell is day live-neighbors ;; counts how many neighboring cells are alive previous-color ] to setup-blank clear-all ;;clears the tick counter along with everything else ask patches [ cell-night ] reset-ticks end to setup-random clear-all ask patches [ ifelse random-float 100.0 < initial-density [ cell-day ][ cell-night ] ] reset-ticks end to cell-day set day? true set pcolor yellow end to cell-night set day? false set pcolor black end to go set previous-intensity count patches with[day?] / count patches ask patches [ set live-neighbors count neighbors with [day?] ] ;;The first ask updates all patches live neighbors before they execute which ;;keeps all the patches in synch with each other ask patches[set previous-color pcolor] ask patches [ ifelse live-neighbors = 3 or live-neighbors = 6 or live-neighbors = 7 or live-neighbors = 8 [ cell-day ] [ if (live-neighbors != 4) [ cell-night ] ] ] tick end to draw-cells let erasing? [day?] of patch mouse-xcor mouse-ycor while [mouse-down?] [ ask patch mouse-xcor mouse-ycor [ ifelse erasing? [ cell-night ] [ cell-day ] ] display ] end @#$#@#$#@ GRAPHICS-WINDOW 159 10 613 485 55 55 4.0 1 10 1 1 1 0 1 1 1 -55 55 -55 55 1 1 1 ticks 15.0 SLIDER 3 348 146 381 initial-density initial-density 0.0 100.0 51.8 0.1 1 % HORIZONTAL BUTTON 11 68 113 101 NIL setup-random NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 7 245 110 283 go-once go NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 8 295 111 333 go-forever go T 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 4 392 150 437 Percentage Current Density (count patches with[day?] / count patches) * 100 2 1 11 BUTTON 11 32 113 65 NIL setup-blank NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 12 123 114 193 When the draw-cells is down, it enables you to add or remove cells by holding down the mouse button at the desired location. 11 0.0 0 BUTTON 7 201 110 236 NIL draw-cells T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 754 246 1184 465 Intensity Varying with Time Time Percentage Intensity Variation 0.0 100.0 0.0 100.0 true false "" "" PENS "default" 1.0 2 -16777216 true "" "plot (count patches with [day?] / count patches) * 100" PLOT 622 11 962 236 Rate of Change in Intensity over Time Time Percentage Change in Intensity 0.0 10.0 0.0 5.0 true false "plot 0" "" PENS "default" 1.0 0 -16777216 true "" "if ticks > 2\n[plot ((count patches with [day?] / count patches) - previous-intensity) * 100]" PLOT 972 11 1311 236 Rate of Change Over Time NIL Percentage Change in Cells 0.0 10.0 0.0 40.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "plot (count patches with [pcolor != previous-color] / count patches) * 100" @#$#@#$#@ ## WHAT IS IT? This program models a two-dimensional cellular automaton. This particular cellular automaton is called Day and Night. Cellular automata (CA) were invented in the 1940s by Stanislaw Ulam and John von Neumann to prove that self-reproduction is possible in machines and to further link biology and compuatation. A CA is a collection of cells arranged in a grid, such that each cell changes state as a function of time according to a defined set of rules that includes the states of neighboring cells. In other words, a cellular automaton can thought of as computational machine performing actions based on specified rules. These are idealized models of complex systems as they consist of large network of simple components with limited communication among components and no central control. Cellular automata result complex dynamics from simple rules. The rule modeled here is given the name "Day & Night" because both its states states are symmetric meaning if all states are switched if on, turn off vise versa the automata will proceed in the same manner. As with Conway ’s Life the automaton model here displays Class IV Behavior. Although the day and night rule set is classified as a chaotic cellular automaton, it behaves very differently from Conway's original rules because of its unique properties. ## HOW IT WORKS The day and night rule set is as follows. Each cell checks the state of itself and its eight surrounding neighbors and then sets itself to either alive or dead. If there are less than two alive neighbors, then the cell dies. In this cellular automaton, a living cell survives if it has 3, 4, 6, 7, or 8 neighbors and a dead cell becomes alive when it has 3, 6, 7, or 8 neighbors (otherwise, a cell remains in the same state). This is done in parallel and continues forever. It exhibits complex behavior similar to Conway's Game of Life : there exist numerous well-known guns and small oscillators as well as spaceships formed by combining oscillators in such a way that they periodically emit spaceships of various types ## HOW TO USE IT The INITIAL-DENSITY slider determines the initial density of cells that are alive. SETUP-RANDOM initializes the model with a percentage of the cells alive. The percentage alive cells is determined by the INITIAL-DENSITY slider. GO-FOREVER runs the model with rule set forever. GO-ONCE runs the model with rule set once. If you want to draw your own pattern, use the DRAW-CELLS button and then use the mouse to "draw" and "erase" in the view. ## THINGS TO NOTICE Find stable shapes that are motionless. Also, notice any recurring shapes. Observe how the population dynamics changes in each intialization and the how quickly each leads to a different stable point. Notice how the chaotic structures gradually consdilate into large regions of living and dead cells with constantly shifting boundaries with activity which mirrors the behaviour of other regions. Observe how the intensity of living cells affect the population dynamics in any particular simulation. Compare the same to Conway's orginal rule set. Do intializations stablize relatively quickly? View the PERCENTAGE CURRENT DENSITY monitor to see the current value of density of living cells. ## THINGS TO TRY Is it possible for this cellular automata to be used to compute anything? How? Try to build various objects which don't die (using DRAW-CELLS). Try to change the shape of grid and see how it affects the steady state as well as the time to reach it. ## EXTENDING THE MODEL Modify the rules of the model to simulate different complex behaviours and observe the resulting character of a given rule set. ## CREDITS The author would like to acknowledge Mr. Rinkaj Goyal, USICT for his guidance and support which has been immense help in understanding the fundamentals of Netlogo and complex systems as well as provided motivation to carry out authentic and valuable research. ## REFERENCES e-mail: abhigenie92@gmail.com Day & Night was invented and named by Nathan Thompson in 1997, and later explored and discussed by David I. Bell. Bell, David I. (1997), Day & Night - An Interesting Variant of Life Pete Carlton. "Pete's Game of Life Page: B3678 S34678 Variations on Conway’s Game of Life and Other Cellular Automata ,David Hua and Martin Pelikan Life model in Netlogo library was particularly helpful for reference. @#$#@#$#@ 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 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