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Brownian Motion Maze Solving (based on "The Dumbest Way To Solve A Maze")

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POSTED BY: Moderation Team

The way you derive the uniform distributions, choosing the coordinates describing lines... these are the descriptions of lines! It is similar to the foundation of a cellular automaton based on And. When you focus on it you can see the balls diverge at the beginning, decide to run the simulation so many times to catch the end motion, decrease the end-difficulty (that's 2000 balls but no walls). Brownian Motion looks like maze-solving? No way! That's awesome.

Brownian Motion like Maze Solving

g = GridGraph[{8, 12}];
spanningTree = 
 FindSpanningTree[
  NeighborhoodGraph[g, RandomSample[VertexList[g], 8*12], 1]]

The Boolean of wall membership, sowing the position parts (showing how we can get the positionSeries to show the path for one particle) and traversing... this simulation is definitely super fun it's like the ball that went to the maze start versus the one that escaped the maze is not the same! And then we've got these successor balls coming in and updating.

ListPlot[
Flatten[
Table[Transpose@
RandomFunction[WienerProcess[\[Mu], \[Sigma]], {0, 1, .001}, 2][
"States"], {\[Mu], .001, 1, .1}, {\[Sigma], .001, 1, .1}]], 
PlotTheme -> "Detailed", PlotRange -> Full, 
ColorFunction -> "Rainbow", ImageSize -> 300]

Brownian Motion Simulator

Thank you for posting this dynamic content! I was inspired by and would also like to thank James, Donavon, and Varun for their helpful demonstrations. Ya know how philosophy symbolically reduces to explain the nature of everything... and in this simulation the balls are hopping and bouncing at all pseudorandom velocity, in a maze. What would you do if you could generate a new FindSpanningTree and GridGraph to in form form the passages and walls? It's a beautiful topic and explanation to us, as a resource for vector art.

https://reference.wolfram.com/language/example/BrownianMotion.html

https://demonstrations.wolfram.com/BrownianMotionPathAndMaximumDrawdown/

https://demonstrations.wolfram.com/ExitTimesOfBrownianMotionIn3D/

https://demonstrations.wolfram.com/BrownianMotionIn2DAndTheFokkerPlanckEquation/

https://demonstrations.wolfram.com/TwoDimensionalFractionalBrownianMotion/

POSTED BY: Dean Gladish
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