There certainly are viable outcomes, for example you could imagine the cube as two facing squares each end independent of each other. Ants moving are independent events. I'm trying to figure out the multiple weaving pattern form, I'm trying anemone and weave plugins in grasshopper but not having much luck, I'd appreciate any links to similar scripts, insights or ideas you have on how to script this, including using any grasshopper plugins! There is an ant on each vertex of a pentagon called. We can label the ants A, B, and C and represent their directions as either "L" for left or "R" for right. Out of these 2^n possible outcomes, there are (n + 1)/2 outcomes where none of the ants collide. What is the probability that they don't collide? If you're curious what ChatGPT made of this puzzle...
Which of the following instructions is an unconditional branch a JSR b JMP c BRz. © Nigel Coldwell 2004 - – The questions on this site may be reproduced without further permission, I do not claim copyright over them. But that sadly is not the full story. Similarly with cdab and dcba involve swaps c & a and d & a respectively. AssumptionsI think it's fairly clear that there are no real ants, the ants are just a device for explaining the puzzle. Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e. g., in search results, to enrich docs, and more. With three things each having two choices we have 2x2x2 = 8 possible configurations. A pentagon has how many vertices. It appears they are using a voroni/de launy or similar pattern as the texture within the form. For a triangular based pyramid an ant at any of the 4 vertices can travel to each and every other vertex. We can see trivially that for a square the answer will be 1/8. Thus the probability that the ants will not collide. There are 4 ants and each has 3 possible destinations meaning there are 34 = 81 possible outcomes.
The question is how many of these don't involve a collision... We assume the ants have a 50/50 chance of picking either direction. I always think it's arrogant to add a donate button, but it has been requested. Therefore, the probability that none of the ants collide in a square is 6/16 = 3/8 or 37. This problem looks quite hard but turns out to be fairly easy. Another extensionThe next obvious extension is to consider four ants on a tetrahedron or triangular based pyramid. These neurotransmitters fit into special receptor sites on the dendrites of the. If n = 8, OCTAGON.. Continuous weave pattern with multiple layers - Grasshopper. e., 8 ants positioned at 8 corners are started moving towards other possible corners. Square, N sided PolygonUsing the first approach for the triangle we had 2•½•½•½ or 2•(½^n) or 1/2n-1 or 2-(n-1) where n was equal to 3.
If I help you get a job though, you could buy me a pint! The ants will not collide if all the ants are either moving in the clockwise direction or all the N ants are either moving in the anticlockwise direction. Probability that all the ants move in the clockwise direction + Probability that all the ants move in the anticlockwise direction. The answers are mine and may not be reproduced without my expressed prior consent. Answer: Step-by-step explanation: Each ant has only two option to move, either in the clockwise direction or in the anticlockwise direction. I'm not sure of the best way to work this out, but I will... There is an ant on each vertex of a pentagon form. Either all clockwise or all anticlockwise. If each ant moves randomly, there are 2 possible directions for each ant, so there are 2^n possible outcomes for the directions of the ants. Instead I used a spread sheet to show all the outcomes in which each ant moves and count how many of the outcomes involved a unique ant on each vertex. I believe these are called derangements. ) Course Hero member to access this document. Upload your study docs or become a. Get help with your Polygons homework.
Hi everyone, I'm very interested in understanding how a pattern like this was generated using grasshopper: It looks like the kind of beautiful work that nervous system do but I didn't see this particular design there. For a square, the same problem can be analyzed similarly. Once approved by the Capital Committee the Sponsor will meet with the Project. The cube is even more complicated, 8 ants or vertices each with 3 possible destinations gives 6, 561. The thing which helped me figure out a neat way of doing it was looking at this page and you'll find a similar example with some mathematica code attached Math Artwork. When you make the shape for one vertex it is radial symmetry, three vertexes from three pentagon; then you orient on each pentagon. Similarly ants placed in any corner can move in 2 directions. 4 SIMULATION RESULTS Our simulations were performed with the model presented in. 2/2n brings us to 1/2n-1. In all other outcomes, at least two of the ants will collide. Please inquire using the link at the top of the page. There are 'n' ants at 'n' corners of a 'n' sided closed regular polygon, they randomly start moving towards another corner that is adjacent to it? Can't find the question you're looking for? I then found it was simpler to think about it in terms of pentagons and triangles & using an icosahedron as the base shape.
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