---p1_particle_behavior_3.nlogo

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globals [  clock tick-length          ;; clock variables.  box-edge                   ;; distance of box edge from axes.  tracked-particle           ;; particle we're currently tracking.  duration                   ;; set from Pedagogica.  avg-speed                  ;; average current speed of all the particles.  avg-speed-history          ;; history of average speed over the model run.  avg-avg-speed              ;; average of avg-speed over time.  num-speed-changes          ;; how many times the tracked-particle has changed                             ;; speed.]breeds [ particles ]particles-own [  speed mass                 ;; particle info  last-collision]to setup  ca  set-default-shape particles "circle"  set clock 0  set duration 0  ;; box has constant size...  set box-edge (screen-edge-x - 1)  make-box  make-particles  set tracked-particle nobody  set avg-speed-history []  update-avg-speedendto go  locals [old-clock]  ;; the model stops after DURATION clock ticks.  if (clock >= duration)  [    set avg-avg-speed (mean avg-speed-history)    stop  ]  ask particles [ bounce ]  ask particles [ move ]  ask particles    [ ;; without-interruption is needed here so one collision is      ;; happening at a time      without-interruption	[ check-for-collision ] ]  set old-clock clock  set clock clock + tick-length  if (floor clock) != (floor old-clock)    [ update-avg-speed ]  set tick-length 1 / (ceiling max values-from particles [speed])endto update-avg-speed  set avg-speed (mean values-from particles [speed])  set avg-speed-history (lput avg-speed avg-speed-history)endto bounce  ;; particle procedure  locals [new-px new-py]  ;; if we're not about to hit a wall (yellow patch), or if we're already on a  ;; wall, we don't need to do any further checks  if pcolor = yellow or pcolor-of patch-at dx dy != yellow     [ stop ]  ;; get the coordinates of the patch we'll be on if we go forward 1  set new-px round (xcor + dx)  set new-py round (ycor + dy)  ;; if hitting left or right wall, reflect heading around x axis  if (abs new-px = box-edge)    [ set heading (- heading) ]  ;; if hitting top or bottom wall, reflect heading around y axis  if (abs new-py = box-edge)    [ set heading (180 - heading) ]endto move  ;; particle procedure  if patch-ahead (speed * tick-length) != patch-here    [ set last-collision nobody ]  jump (speed * tick-length)endto check-for-collision  ;; particle procedure  locals [ candidate ]  if count other-particles-here >= 1  [    ;; the following conditions are imposed on collision candidates:    ;;   1. they must have a lower who number than my own, because collision    ;;      code is asymmetrical: it must always happen from the point of view    ;;      of just one particle.    ;;   2. they must not be the same particle that we last collided with on    ;;      this patch, so that we have a chance to leave the patch after we've    ;;      collided with someone.    set candidate random-one-of other-particles-here with      [who < who-of myself and myself != last-collision]    ;; we also only collide if one of us has non-zero speed. It's useless    ;; (and incorrect, actually) for two particles with zero speed to collide.    if (candidate != nobody) and (speed > 0 or speed-of candidate > 0)    [      collide-with candidate      set last-collision candidate      set last-collision-of candidate self      ;; we want to keep track of how many times the tracked-particle       ;; changes speed. only collisions change the speed of a particle.      if self = tracked-particle or candidate = tracked-particle         [ set num-speed-changes num-speed-changes + 1 ]    ]  ]end;; tracks the specified particle, if no particle is currently being tracked.;; if there's no such particle, it just prints a warning to the command;; center.to track-particle [n]  ifelse tracked-particle != nobody  [    print "You are already tracking particle " + who-of tracked-particle  ]  [    ifelse (turtle n) = nobody     [      print "There is no such particle!"    ]    [      set tracked-particle (turtle n)      ask tracked-particle [ pen-down ]      print "Now tracking particle " + who-of tracked-particle    ]  ]end;; implements a collision with another particle.;;;; THIS IS THE HEART OF THE PARTICLE SIMULATION, AND YOU ARE STRONGLY ADVISED;; NOT TO CHANGE IT UNLESS YOU REALLY UNDERSTAND WHAT YOU'RE DOING!;;;; The two particles colliding are self and other-particle, and while the;; collision is performed from the point of view of self, both particles are;; modified to reflect its effects. This is somewhat complicated, so I'll;; give a general outline here: ;;   1. Do initial setup, and determine the heading between particle centers;;      (call it theta).;;   2. Convert the representation of the velocity of each particle from;;      speed/heading to a theta-based vector whose first component is the;;      particle's speed along theta, and whose second compenent is the speed;;      perpendicular to theta.;;   3. Modify the velocity vectors to reflect the effects of the collision.;;      This involves:;;        a. computing the velocity of the center of mass of the whole system;;           along direction theta;;        b. updating the along-theta components of the two velocity vectors.;;   4. Convert from the theta-based vector representation of velocity back to;;      the usual speed/heading representation for each particle.;;   5. Perform final cleanup and update derived quantities.to collide-with [ other-particle ] ;; particle procedure  locals  [    ;; local copies of other-particle's relevant quantities    mass2 speed2 heading2     ;; quantities used in the collision itself    theta   ;; heading of vector from my center to the center of other-particle.    v1t     ;; velocity of self along direction theta    v1l     ;; velocity of self perpendicular to theta    v2t v2l ;; velocity of other-particle, represented in the same way    vcm     ;; velocity of the center of mass of the colliding particles,            ;;   along direction theta  ]    ;;; PHASE 1: initial setup  ;; for convenience, grab some quantities from other-particle  set mass2 mass-of other-particle  set speed2 speed-of other-particle  set heading2 heading-of other-particle  ;; since particles are modeled as zero-size points, theta isn't meaningfully  ;; defined. we can assign it randomly without affecting the model's outcome.  set theta (random-float 360)  ;;; PHASE 2: convert velocities to theta-based vector representation  ;; now convert my velocity from speed/heading representation to components  ;; along theta and perpendicular to theta  set v1t (speed * cos (theta - heading))  set v1l (speed * sin (theta - heading))  ;; do the same for other-particle  set v2t (speed2 * cos (theta - heading2))  set v2l (speed2 * sin (theta - heading2))  ;;; PHASE 3: manipulate vectors to implement collision   ;; compute the velocity of the system's center of mass along theta  set vcm (((mass * v1t) + (mass2 * v2t)) / (mass + mass2) )  ;; now compute the new velocity for each particle along direction theta.  ;; velocity perpendicular to theta is unaffected by a collision along theta,  ;; so the next two lines actually implement the collision itself, in the  ;; sense that the effects of the collision are exactly the following changes  ;; in particle velocity.  set v1t (2 * vcm - v1t)  set v2t (2 * vcm - v2t)  ;;; PHASE 4: convert back to normal speed/heading  ;; now convert my velocity vector into my new speed and heading  set speed sqrt ((v1t * v1t) + (v1l * v1l))  ;; if the magnitude of the velocity vector is 0, atan is undefined. but  ;; speed will be 0, so heading is irrelevant anyway. therefore, in that   ;; case we'll just leave it unmodified.  if v1l != 0 or v1t != 0    [ set heading (theta - (atan v1l v1t)) ]  ;; and do the same for other-particle  set speed-of other-particle sqrt ((v2t * v2t) + (v2l * v2l))  if v2l != 0 or v2t != 0    [ set heading-of other-particle (theta - (atan v2l v2t)) ]  ;; PHASE 5: final updates  ;; now recolor, since color is based on quantities that may have changed  recolor  ask other-particle    [ recolor ]endto recolor  ;; particle procedure  ifelse speed < (0.5 * 10)  [    set color blue  ]  [    ifelse speed > (1.5 * 10)      [ set color red ]      [ set color green ]  ]end;;;;;; drawing procedures;;;;; draws the boxto make-box  ask patches with [ ((abs pxcor = box-edge) and (abs pycor <= box-edge)) or                     ((abs pycor = box-edge) and (abs pxcor <= box-edge)) ]    [ set pcolor yellow ]end;; creates some particlesto make-particles  create-custom-particles number  [    set speed random-float 20    set mass 1.0    set last-collision nobody    random-position    recolor  ]  set tick-length 1 / (ceiling max values-from particles [speed])end;; place particle at random location inside the box.to random-position ;; particle procedure  setxy ((1 - box-edge) + random-float ((2 * box-edge) - 2))        ((1 - box-edge) + random-float ((2 * box-edge) - 2))  set heading random-float 360end;; make turtles appear more like particlesto-report particle [n]  report turtle nend; *** NetLogo Model Copyright Notice ***;; This model was created as part of the project: CONNECTED MATHEMATICS:; MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL; MODELS (OBPML).  The project gratefully acknowledges the support of the; National Science Foundation (Applications of Advanced Technologies; Program) -- grant numbers RED #9552950 and REC #9632612.;; Copyright 1998 by Uri Wilensky. All rights reserved.;; Permission to use, modify or redistribute this model is hereby granted,; provided that both of the following requirements are followed:; a) this copyright notice is included.; b) this model will not be redistributed for profit without permission;    from Uri Wilensky.; Contact Uri Wilensky for appropriate licenses for redistribution for; profit.;; This model was converted to NetLogo as part of the project:; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN; CLASSROOMS.  The project gratefully acknowledges the support of the; National Science Foundation (REPP program) -- grant number REC #9814682.; Converted from StarLogoT to NetLogo, 2001.  Updated 2002.;; To refer to this model in academic publications, please use:; Wilensky, U. (1998).  NetLogo GasLab Gas in a Box model.; http://ccl.northwestern.edu/netlogo/models/GasLabGasinaBox.; Center for Connected Learning and Computer-Based Modeling,; Northwestern University, Evanston, IL.;; In other publications, please use:; Copyright 1998 by Uri Wilensky.  All rights reserved.  See; http://ccl.northwestern.edu/netlogo/models/GasLabGasinaBox; for terms of use.;; *** End of NetLogo Model Copyright Notice ***@#$#@#$#@GRAPHICS-WINDOW2381149428835353.465110111CC-WINDOW7232180314Command CenterBUTTON651014243go/stopgoT1TOBSERVERTBUTTON7106243NILsetupNIL1TOBSERVERTMONITOR1511822067Numbercount particles01SLIDER74514278numbernumber130010011NILMONITOR15179221128clockfloor clock01MONITOR780140129tracked part. speedspeed-of tracked-particle31MONITOR7181119230average speedavg-speed31MONITOR7130212179tracked part. speed changesnum-speed-changes01@#$#@#$#@(in this section of the interface, information about the model is usually provided) You may freely download NetLogo at your home!Go to our site: http://ccl.northwestern.edu/netlogo/You can view models through a web browser as well:http://ccl.northwestern.edu/netlogo/models/  This model is part of the Connected Chemistry high school curriculum.  Connected Chemistry is currently under development; for more information please refer to:http://ccl.northwestern.edu/curriculum/chemistry/       CREDITS AND REFERENCES----------------------To refer to this model in academic publications, please use: Wilensky, U. (2002).  NetLogo P1_Particle_Behavior_3 model.  http://ccl.northwestern.edu/netlogo/models/P1_Particle_Behavior_3.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.     In other publications, please use: Copyright 2002 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/P1_Particle_Behavior_3 for terms of use.@#$#@#$#@defaulttrue0Polygon -7566196 true true 150 5 40 250 150 205 260 250circlefalse0Circle -7566196 true true 35 35 230@#$#@#$#@NetLogo 2.0.0@#$#@#$#@@#$#@#$#@@#$#@#$#@

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