patches-own [ state next-state ] globals [ colors stateLabels constSList constKList support-factor parasite-state decay-rate ;; the probability a state will be converted to state 0 ticks cnt-parasites movie-dir movie ] ;; for internal testing purposes ;; you can ignore this procedure. to test locals [ p ] if false [ ask patches [set next-state 0] ask patches [set-patchs-next-state] set p patch 0 0 ask p [ set state 0] ask p [ ask patch-at 0 0 [set next-state 1] ] ask p [ ask patch-at 1 0 [set next-state 2] ] ask p [ ask patch-at 0 1 [set next-state 3] ] ask p [ ask patch-at 1 1 [set next-state 4] ] ask patches [set-patchs-next-state] show p show "-------" turn 0 0 ask p [ ask patch-at 0 0 [set pcolor item state colors] ] ask p [ ask patch-at 1 0 [set pcolor item state colors] ] ask p [ ask patch-at 0 1 [set pcolor item state colors] ] ask p [ ask patch-at 1 1 [set pcolor item state colors] ] display ] if true [ ask patches [set next-state 0] ask patches [set-patchs-next-state] set p patch 0 0 ask p [ set state 0] ask p [ ask patch-at 0 1 [set next-state 1] ] ask p [ ask patch-at 1 1 [set next-state 0] ] ask p [ ask patch-at 1 0 [set next-state 3] ] ask p [ ask patch-at 1 -1 [set next-state 4] ] ask p [ ask patch-at 0 -1 [set next-state 5] ] ask p [ ask patch-at -1 -1 [set next-state 6] ] ask p [ ask patch-at -1 0 [set next-state 7] ] ask p [ ask patch-at -1 1 [set next-state 8] ] ask patches [set-patchs-next-state] display ask p [compute-patchs-next-state] ask patches [set-patchs-next-state] show "-----" repeat 100 [ ask patches [set next-state state] patch-diffuse ask patches [set-patchs-next-state] ;ask patches [set pcolor item state colors] ] ] if false [ ask patches [set next-state 0] ask patches [set-patchs-next-state] set p patch 0 0 ask p [ set state 0] ask p [ ask patch-at -1 0 [set next-state 1] ] ask p [ ask patch-at 1 0 [set next-state 2] ] ask p [ ask patch-at 0 -1 [set next-state 3] ] ask p [ ask patch-at 0 1 [set next-state 4] ] ask patches [set-patchs-next-state] show p show "-------" ;;ask p [compute-patchs-next-state] ] if false [ repeat 1000 [ ask random-one-of patches [ set pcolor white ] ] ] end to setup locals [ x y p00 p01 p10 p11 temp index cnt ] ca set decay-rate decay set support-factor 100 set parasite-state 1 set stateLabels ["0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10"] set colors [black red green blue yellow turquoise 6 violet magenta 62 brown] set constSList [0 1 1 1 1 1 1 1 1 1 1] ;; this initialization is for demonstration purposes. This table will be computed by the settings ;; of the sliders. This initialization demonstrates how the table will be setup for hc-states = 0 ;; and no parasites. set constKList [ [0 0 0 0 0 0 0 0 0 0 0] ;; state 0 (black) will be supported by noone [0 0 0 0 0 0 0 0 0 0 100] ;; state 1 will be supported by state 10 with factor 100 [0 100 0 0 0 0 0 0 0 0 0] ;; state 2 will be supported by state 1 with factor 100 [0 0 100 0 0 0 0 0 0 0 0] ;; state 3 will be supported by state 2 with factor 100 [0 0 0 100 0 0 0 0 0 0 0] ;; state 4 will be supported by state 3 with factor 100 [0 0 0 0 100 0 0 0 0 0 0] ;; state 5 will be supported by state 4 with factor 100 [0 0 0 0 0 100 0 0 0 0 0] ;; state 6 will be supported by state 5 with factor 100 [0 0 0 0 0 0 100 0 0 0 0] ;; state 7 will be supported by state 6 with factor 100 [0 0 0 0 0 0 0 100 0 0 0] ;; state 8 will be supported by state 7 with factor 100 [0 0 0 0 0 0 0 0 100 0 0] ;; state 9 will be supported by state 8 with factor 100 [0 0 0 0 0 0 0 0 0 100 0] ;; state 10 will be supported by state 9 with factor 100 ] ;; this initialization is for demonstration purposes. This table will be computed by the settings ;; of the sliders. This initialization demonstrates how the table will be setup for hc-states = 0 ;; parasites and the support-factor-parasite of 2.0. set constKList [ [0 0 0 0 0 0 0 0 0 0 0] ;; state 0 (black) will be supported by noone [0 0 0 0 0 0 0 0 0 0 200] ;; state 1 (parasite) will be supported by state 10 with factor 200 [0 0 0 0 0 0 0 0 0 0 100] ;; state 2 will be supported by state 10 with factor 100 [0 0 100 0 0 0 0 0 0 0 0] ;; state 3 will be supported by state 2 with factor 100 [0 0 0 100 0 0 0 0 0 0 0] ;; state 4 will be supported by state 3 with factor 100 [0 0 0 0 100 0 0 0 0 0 0] ;; state 5 will be supported by state 4 with factor 100 [0 0 0 0 0 100 0 0 0 0 0] ;; state 6 will be supported by state 5 with factor 100 [0 0 0 0 0 0 100 0 0 0 0] ;; state 7 will be supported by state 6 with factor 100 [0 0 0 0 0 0 0 100 0 0 0] ;; state 8 will be supported by state 7 with factor 100 [0 0 0 0 0 0 0 0 100 0 0] ;; state 9 will be supported by state 8 with factor 100 [0 0 0 0 0 0 0 0 0 100 0] ;; state 10 will be supported by state 9 with factor 100 ] ;; recompute constKList due to settings of hc-state ;; first building a list of needed length and filled with 0 set temp [] repeat hc-states + 1 [ set temp fput 0 temp ] set constKList [] set constKList lput temp constKList ;; state 0, will not be supported by anyone ;; set the support factor for the first state. ;; if it is a parasite choose the appropiate factor ;; state 1 will always be supported by the last state set temp replace-item hc-states temp support-factor ;; set the usual support factor if Parasites [ ;; replace it if a parasite is in the hypercycle set temp replace-item hc-states temp (support-factor-parasite * support-factor) ] set constKList lput temp constKList ;; state 1 will be supported by the last state set index 0 ;; set index for computing state 2 set cnt hc-states - 1 ;; the next states will be constructed hc-states-1 times using the loop if Parasites [ ;; but if we have a parasite in the hypercycle set temp replace-item hc-states temp support-factor ;; state 2 will be supported by the last state set constKList lput temp constKList ;; add the support for state 2 set cnt cnt - 1 ;; one loop less because we have computed state 2 set index index + 1 ;; we have already computed a state so inkrement the index ] set temp replace-item hc-states temp 0 ;; set the support factor of the last state to 0 ;; compute state 2 (state 3 if parasite present) and following repeat cnt [ set temp replace-item index temp 0 set index index + 1 set temp replace-item index temp support-factor set constKList lput temp constKList ] show constKList set ticks 0 set movie false movie-end display ;; setting up the patches according to the sliders and ;; switches ask patches [ set next-state 0 if (random 2) > 0 [ ifelse Parasites [ set next-state (random (hc-states - 1)) + parasite-state + 1 ][ set next-state (random hc-states) + 1 ] ] ] ;; ask the patches to accept the new state ;; values ask patches [ set-patchs-next-state ] do-plot end ;; plotting the diagram to do-plot locals [ index cnt ] ;; choose the diagram set-current-plot "count states" set-current-plot-pen item 0 stateLabels set-plot-pen-color item 0 colors ;; Plot the black patches (state 0). Because the state 0 (unused patches) is the dominant ;; state the plotting will be adjusted to the number of used hc-states in this model. plot round (count patches with [state = index] / hc-states) ;; Plot the rest of the states. set index 1 repeat hc-states [ set-current-plot-pen item index stateLabels set-plot-pen-color item index colors set cnt count patches with [state = index] plot cnt ;; Update the parasite count. if Parasites [ if index = parasite-state [ set cnt-parasites cnt ] ] set index index + 1 ] end ;; set the current state to set-patchs-next-state set state next-state set pcolor item state colors end ;; compute the next state of all patches to compute-patchs-next-state locals [ p s state-list temp-states choose-state support support-list kvalues index si i sumValues prob-list prob-interval prob r l ] ;; if this patch is empty (state 0) compute the probability of the next state. The probability is ;; given by the surrounding patches and their states. ifelse state = 0 [ ;; setup list with the 8 neighbours states set state-list [] set support-list [] ;; patch North set p patch-at 0 1 set state-list lput state-of p state-list ;; patch North/West set p patch-at 1 1 set state-list lput state-of p state-list ;; patch West set p patch-at 1 0 set state-list lput state-of p state-list ;; patch West/South -> South/West set p patch-at 1 -1 set state-list lput state-of p state-list ;; patch South set p patch-at 0 -1 set state-list lput state-of p state-list ;; patch South/East set p patch-at -1 -1 set state-list lput state-of p state-list ;; patch East set p patch-at -1 0 set state-list lput state-of p state-list ;; patch East/North -> North/East set p patch-at -1 1 set state-list lput state-of p state-list ;; now the states of all surrounding neigbours are stored in a state-list. The neighbours states ;; 8 1 2 ;; 7 x 3 ;; 6 5 4 ;; will result in a list [1 2 3 4 5 6 7 8] ;; extend the list on both sides by two elements ;; to make this list quasi-cyclic set temp-states state-list set state-list fput (item 7 temp-states) state-list set state-list fput (item 6 temp-states) state-list set state-list lput (item 0 temp-states) state-list set state-list lput (item 1 temp-states) state-list ;; now the list contains the states (referring to the example) ;; [7 8 1 2 3 4 5 6 7 8 1 2] ; show plist ; show state-list ;; state-list: List of all states of the neighbours (excluding myself) in the order ;; East NorthEast North NorthWest West SouthWest South SouthEast East NorthEast North NorthWest ;; ;; support-list: List with the computed abilities for each neighbour to reproduce into ;; an empty patch (state 0) ;; ;; p: temporary patch variable ;; ;; s: temporary state variable of p ;; ;; temp-states: Temporary list with states. In this list every loop one of the neighbours (the ;; current one) will be removed. ;; ;; kvalues: Support values for the current neighbour ;; ;; support: The abilities of a neighbour to fill an empty patch (state 0) ;; set support-list [] set choose-state [] set si 2 ;; Access index for states. Starts with 2 due to quasi cyclic list to start north repeat 4 [ ;; four neighbours (north, west, south, east) set s item si state-list ;; get the state of the current neighbour ;; the current state has a certain probability to reproduce itself. The probability ;; is computed by the reproduction rate, stored in constSList, and the support of the ;; surrounding states. Which state supports the current state by which value is stored ;; in constKList set choose-state lput s choose-state ;; add the state for the list of chooseable states for the current patch set support item s constSList ;; get the support factor for reproducing itself set s item (item si state-list) constKList ;; get the support activity by other states for the current state ;; Now compute the support of the neighbours for this state. set i -2 repeat 5 [ set support (support + item (item (si + i) state-list) s) set i (i + 1) ] ;; Append computed value to the end of the list of all support values. set support-list lput support support-list set si (si + 2) ] ;; set the state-list to the chooseable states set state-list choose-state ;; now all abilities for every neighbour to fill an empty patch are computed ;; compute now the probabilities for all neighbours to be choosen to fill an ;; empty patch or the patch stayes empty set support-list fput 11 support-list ;; the support value an empty patch remains empty set state-list fput 0 state-list ;; store the empty state (=0) in the list of possible states set sumValues sum support-list ;; summarize all support values ;; compute the probability a state in this prob-list is choosen set prob-list [] set index 0 foreach support-list [ set prob-list lput ((item index support-list) / sumValues) prob-list set index index + 1 ] ; show prob-list ;; compute the probability interval set prob-interval [] ;; empty list set prob 0 foreach prob-list [ set prob prob + ? set prob-interval lput prob prob-interval ] set prob-interval but-last prob-interval ;; remove the last entry (should be 1.0) but due to ;; floating point arithmetik you can't be sure set prob-interval lput 1.0 prob-interval ;; add 1.0 as the upper limit set r random-float 1 ;; choose a random number [0..1[ ;; find the probability intervall this random number fits in ;; the interval correponds to the probability a state is chosen set index 0 set l item index prob-interval while [r > l] [ set index index + 1 set l item index prob-interval ] set next-state item index state-list ] [ ;; This patch is not empty. Compute the probability the patch will be empty. if (random-float 1) < decay-rate [ set next-state 0 ] ] end ;; randomly add parasites to do-add-parasites ifelse Parasites [ repeat add-parasites [ ask random-one-of patches [ set next-state parasite-state set-patchs-next-state ] ] do-plot ] [ user-message "Please turn on the parasites feature first." ] end to go ;; run the model one-cycle end to movie-setup set movie false movie-end ;; prompt user for movie location set movie-dir user-choose-directory if not is-string? movie-dir [ stop ] ;; stop if user canceled set-current-directory movie-dir movie-start "capture.mov" no-display set movie true end to movie-end ifelse movie [ ifelse movie-status != "No movie." [ ;; export the movie movie-close print "Exported movie to " + movie-dir ][ user-message "Movie contained no frames and will not be saved." ] set movie false ] [ if movie-status != "No movie." [ show "movie-status: " + movie-status user-message "After releasing this dialog the current movie will be saved as 'capture.mov' and will overwrite any existing file." movie-close ] ] end to go-for repeat cycles [ go ] end to one-cycle without-interruption [ ask patches [ compute-patchs-next-state ] patch-diffuse ask patches [ set-patchs-next-state ] ] set ticks ticks + 1 do-plot if movie [ movie-grab-graphics ] ifelse frame-skip > 0 [ if ticks mod frame-skip = 0 [ display ] no-display ][ display ] end ;; diffuse a 2x2 block clockwise or counter-clockwise ;; ;; The block 12 will be to 41 and the block 12 will be to 23 ;; 43 32 43 14 ;; this a procedure published by Toffoli and Margolus to simulate the diffusion in ;; a gas. The 2x2 blocks will be turned by random in one direction. Usually a second ;; run will be done but this time with a offet of one to the previous run so a 2x2 block ;; shifted by one in each direction patch will be choosen. to turn [x y] locals [ p00 p01 p10 p11 h-state ] ;;show "turn: " + x + " " + y set p00 patch-at x y set p01 patch-at (x + 1) y set p10 patch-at x (y + 1) set p11 patch-at (x + 1) (y + 1) ifelse (random 2) > 0 [ ;; turn patches clockwise ;; show "clockwise" set h-state next-state-of p00 set next-state-of p00 next-state-of p01 set next-state-of p01 next-state-of p11 set next-state-of p11 next-state-of p10 set next-state-of p10 h-state ] [ ;; turn patches counter clockwise ;; show "counter clockwise" set h-state next-state-of p00 set next-state-of p00 next-state-of p10 set next-state-of p10 next-state-of p11 set next-state-of p11 next-state-of p01 set next-state-of p01 h-state ] end ;; diffuse the patches by a double run (Toffoli and Margolus) to patch-diffuse locals [ x0 y0 x y run-x run-y ] set x0 0 - screen-edge-x set y0 0 - screen-edge-y set run-x (screen-edge-x + 1) set run-y (screen-edge-y + 1) set y y0 repeat run-y [ set x y0 repeat run-x [ turn x y set x x + 2 ] set y y + 2 ] set y0 y0 + 1 set x0 x0 + 1 set y y0 repeat run-y [ set x y0 repeat run-x [ turn x y set x x + 2 ] set y y + 2 ] end @#$#@#$#@ GRAPHICS-WINDOW 596 10 1007 442 200 200 1.0 1 10 1 1 1 0 CC-WINDOW 5 456 1016 551 Command Center BUTTON 140 10 234 43 NIL setup\n NIL 1 T OBSERVER T NIL BUTTON 140 45 234 78 open movie movie-setup NIL 1 T OBSERVER NIL NIL PLOT 1 172 591 442 count states ticks count 0.0 10.0 0.0 10.0 true true PENS "0" 1.0 0 -16777216 true "1" 1.0 0 -16777216 true "2" 1.0 0 -16777216 true "3" 1.0 0 -16777216 true "4" 1.0 0 -16777216 true "5" 1.0 0 -16777216 true "6" 1.0 0 -16777216 true "7" 1.0 0 -16777216 true "8" 1.0 0 -16777216 true "9" 1.0 0 -16777216 true "10" 1.0 0 -16777216 true MONITOR 533 119 590 168 NIL ticks 5 1 SLIDER 3 10 115 43 hc-states hc-states 1 10 9 1 1 NIL SWITCH 3 45 115 78 Parasites Parasites 0 1 -1000 BUTTON 140 80 234 113 close movie movie-end NIL 1 T OBSERVER T NIL BUTTON 237 10 330 43 NIL one-cycle NIL 1 T OBSERVER T NIL BUTTON 140 115 234 148 add parasites do-add-parasites NIL 1 T OBSERVER T NIL BUTTON 237 45 330 78 NIL go-for NIL 1 T OBSERVER T NIL CHOOSER 332 45 424 90 cycles cycles 1 2 5 10 20 50 100 200 500 1000 2000 5000 10000 20000 50000 6 MONITOR 460 119 529 168 Parasites cnt-parasites 5 1 SLIDER 3 80 115 113 support-factor-parasite support-factor-parasite 0.1 5 2.0 0.1 1 NIL CHOOSER 237 116 330 161 add-parasites add-parasites 1 2 5 10 20 50 100 200 500 1000 2000 5000 10000 20000 50000 9 BUTTON 237 80 330 113 NIL go T 1 T OBSERVER T NIL SLIDER 432 10 544 43 frame-skip frame-skip 0 100 5 1 1 NIL SLIDER 3 116 115 149 decay decay 0 1 0.2 0.01 1 NIL @#$#@#$#@ WHAT IS IT? ----------- This model simulates a hypercycle described by Eigen and Schuster 1979. A hypercycle is a prebiotic model which shows how stable structures (e.g. life forms) can or will emerge because of cyclic support of self replicating molecules to other self replicating molecules. This model can simulate up to 10 different molecule types. The original concept of a hypercycle was critized by John Maynard Smith because a parasite molecule will destroy a hypercycle. Hogeweg and Boerlijst showed 1990 by using a cellular automata a hypercycle will be stable despite by an 'infection' of a parasite because of the spatial structures a hypercycle will emerge. Rules: a) A cell (patch) filled with a molecule (state > 0) has in every cycle a certain chance to become empty (denoted by state 0). This probability is given by the global constant decay (slider). b) Every empty cell (patch) can be filled by a molecule of the surrounding neighbours (north, west, south, east) or remains empty. c) Every molecule has in a cycle of a run a certain chance to reproduce itself. This is defined by the constant s[i] where [i] denotes the i_th entry for the corresponding molecule i. The value for every s[i] is 1. d) Due to the hypercycle a molecule gets some support to reproduce itself if its predecessor is in the neighbourhood. This support value is 100 which raises the probability a molecule will reproduce itself into an empty cell. e) Using a parasite molecule will give more support of one state to the parasite state as any other state will receive. HOW IT WORKS ------------ This model uses no turtles. The patches are the cells of the cellular automata. The models runs through every patch for which the next state will be computed. After all some sort of diffusion to simulate the molecule drift is computed by exchanging the next states of neigbour patches. After all next states have been computed als patches set these as the current state. The state 0 (displayed black) denotes an empty patch. The state 1 (red) will denote a parasite molecule if the parasite option is activated. The parasite will be simulated by changing the support values. Usually the support for 5 states is: 1 supports 2. 2 supports 3. 3 supports 4. 4 supports 5. 5 supports 1. Introducing a parasite will change these rules to 1 supports none. 2 supports 3. 3 supports 4. 4 supports 5. 5 supports 1 and 2. The support of 5 for 1 is higher than the support of 5 for 2. For the general idea how this model works please refer to Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites. Physica D, 48: 17-28. You'll find a link to a pdf document containing this artice at the end of this page. HOW TO USE IT ------------- Use the control elements from top to down and left to right. But read the following information first! Doing a run: Press set-up. Press open-movie if you like to save a movie. Press go. Press go again. Press close-movie (if you have pressed open-movie before). SLIDERS: hc-states: Number of hypercycle states which are used in the current settings. This slider is only effective pressing the setup button. support-factor-parasite: The support factor a parasite is given by the last state. frame-skip: To accelerate display frames can be skipped. n frames are skipped during display where n denotes the value of the slider. A value of 0 will skip no frame. SWITCHES: Parasites: Only effective during pressing the setup button. If parasites are used in this model the state 1 will be the parasite state. The internal tables become different values according to run a parasite state in this model or not. BUTTONS: setup: The setup button initialize the model. Some internal tables are computed according to the settings of some sliders and switches. The number of states, which can't be changed later on, in this model is set pressing the setup button; also the patches are randomly initialized with states. open movie: Rudimentary support for movies. Pressing this button a movie file will be created. You can only choose the path. Open a movie will only write the graphical output of the patches into the movie file. IMPORTANT: Open a movie AFTER you have setup the simulation. close movie: Closes the movie and writes the movie with the name 'capture.mov' in the prior selected directory. add parasites: Adds the number of parasites defined by the choice add-parasites to the model. This button is only effective if the switch 'Parasites' has been turned on during pressing the setup button. The patches are choosen randomly so there is no guarantee exactly 'add-parasites' number of patches will be 'converted' to a parasite. one cycle: Running this model exactly one cycle. go-for: Running this model exactly for the number of cycles given in the choice 'cycles'. go: Running this model forever until this button is pressed again. THINGS TO NOTICE ---------------- Wait for the emerging spirals. This model may run very slowly but structures will emerge only with screen-sizes greater 50. THINGS TO TRY ------------- This section could give some ideas of things for the user to try to do (move sliders, switches, etc.) with the model. EXTENDING THE MODEL ------------------- This section could give some ideas of things to add or change in the procedures tab to make the model more complicated, detailed, accurate, etc. NETLOGO FEATURES ---------------- This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab. It might also point out places where workarounds were needed because of missing features. RELATED MODELS -------------- This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest. CREDITS AND REFERENCES ---------------------- This model was developed by Joerg Hoehne in September 2004 in the intention to learn the concepts and programming features of NetLogo. email: hoehne@thinktel.de Any suggestions, questions, bug reports, corrections (especially typos, grammar, unknown words etc.) and feedback are welcomed. References: [Book, out of print] Gerhard, Martin ; Schuster, Heike: Das digitale Universum. Vieweg Verlag, 1995 [Book, out of print] Eigen, Manfred ; Schuster, Peter: The Hypercycle - A Principle of Natural Self-Organization. Springer, 1979 [link]: http://www-binf.bio.uu.nl/publications/1991.html where you find the following interesting link to http://www-binf.bio.uu.nl/pdf/Boerlijst.pd91-48.pdf Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites. 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