This uses the same motion updating in the previous post, but replaces the contraction step (i.e., boidLocations = 0.995 boidLocations) with a projection to the sphere. Because location is constrained, the step away from the “enemy” can be larger and things don’t fly away, making it too large destroys the flocking behavior.

In response to the request here: https://mathematica.stackexchange.com/q/312395
See other part here:
Boids 1: 3D dynamics, velocity-color mapping, and inertia-driven coordination
Boids 3: periodic domain eliminates edge effects via rectangular lattice projections

A graphic to help with the visualization

In[]:=

sphereGraphic=

With[

]

;

SeedRandom[0];initialize[1000,"Initial Locations"->"Sphere"];friendMobility=0.02;enemyMobility=0.01;swtichFrequency=0.9;everyonesFriend=ConstantArray[randomBoid,numberBoids];everyonesFriendSwitchFrequency=.8;everyonesFriendMobility=0.0001;{nothing,frames}=ReapDoIf[RandomReal[]<(1-swtichFrequency),switchFriendsEnemies];If[RandomReal[]<(1-everyonesFriendSwitchFrequency),everyonesFriend=ConstantArray[randomBoid,numberBoids]];vLast=boidVelocity;boidVelocity=friendMobilityboidForceTerm[friend]-enemyMobilityboidForceTerm[enemy]+everyonesFriendMobilityboidForceTerm[everyonesFriend];vMean=0.5(vLast+boidVelocity);boidLocations=Normalize/@(boidLocations+vMean);SowShowGraphics3D[sphereGraphic],drawBoid[boidLocations,vMean,"Velocity Range"->{.0001,.025},PlotRange->1],

,{t,0,2000};

It can be helpful to turn the graphics objects into images in parallel

In[]:=

LaunchKernels[];AbsoluteTiming[Block[{images},Echo[AbsoluteTiming[images=ParallelMap[Image,Rest@Flatten[frames]];]];Export[FileNameJoin[{NotebookDirectory[],"boidsOnSphere.mp4"}],images]];]

»

{41.1688,Null}

Out[]=

{49.601,Null}

(*boidsOnSphere=FrameListVideo[Flatten[frames]]*)

Out[]=

You can get the mp4 video here:

Import["http:pruffle.mit.edu/~ccarter/Videos/boidsOnSphere.mp4"]

CITE THIS NOTEBOOK

Boids 2: spherical projection with dynamic viewpoint tracking
by W. Craig Carter
Wolfram Community, STAFF PICKS, June 24, 2025
https://community.wolfram.com/groups/-/m/t/3485041