File:Lawoflargenumbersanimation.gif
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Lawoflargenumbersanimation.gif (100 × 169 pixels, file size: 50 KB, MIME type: image/gif, looped, 220 frames, 17 s)
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[edit]DescriptionLawoflargenumbersanimation.gif |
English: Simulation illustrating the Law of Large Numbers. Each frame, you flip a coin that is red on one side and blue on the other, and put a dot in the corresponding column. A pie chart notes the proportion of red and blue so far. Notice that the proportion varies a lot at first, but gradually approaches 50%. Animation made in Mathematica--I'm happy to give you the source code if you want to improve the animation or for any other reason. |
Date | |
Source | Own work |
Author | Sbyrnes321 |
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[edit]Public domainPublic domainfalsefalse |
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
(* Source code written in Mathematica 6.0, by Steve Byrnes, 2010. I release this code into the public domain. *) SeedRandom[1] NumBalls = 500; (*Build list of point coordinates and radii*) BuildCoordList[LeftX_, RightX_, BotY_, TopY_, Cols_, Rows_] := Flatten[Table[{i, j}, {j, BotY, TopY, (TopY - BotY)/(Rows - 1)}, {i, LeftX, RightX, (RightX - LeftX)/(Cols - 1)}], 1]; BlueCoordsList = BuildCoordList[.15, .85, .15, 4.75, 5, 24]; RedCoordsList = BuildCoordList[1.15, 1.85, .15, 4.75, 5, 24]; radius = .05; (*Draw borders*) lines = {Line[{{0, 0}, {0, 5}}], Line[{{1, 0}, {1, 5}}], Line[{{2, 0}, {2, 5}}], Line[{{0, 0}, {2, 0}}]}; (*Draw pie chart*) DrawPie[CenterX_, CenterY_, Radius_, FracRed_] := {{Red, Disk[{CenterX, CenterY}, Radius, {-FracRed \[Pi], FracRed \[Pi]}]}, {Blue, Disk[{CenterX, CenterY}, Radius, {FracRed \[Pi], 2 \[Pi] - FracRed \[Pi]}]}}; (* Randomly generate order that red and blue appear *) AppearOrder = Table[RandomInteger[{0, 1}], {i, 1, NumBalls}]; (* Calculate number of red and blue balls at any given time, and their proportions. *) NumAppeared[time_] := Floor[time]; NumRed[time_] := Total[AppearOrder[[1 ;; NumAppeared[time]]]]; NumBlue[time_] := NumAppeared[time] - NumRed[time]; FracRed[time_] := NumRed[time]/NumAppeared[time]; (* Put everything together! *) Video = {}; NumFrames = 220; For[frame = 1, frame <= NumFrames, frame++, t = frame; ImageGraphicsList = lines; For[pt = 1, pt <= NumBlue[t], pt++, ImageGraphicsList = Append[ImageGraphicsList, {Blue, Disk[BlueCoordsList[[pt]], radius]}]]; For[pt = 1, pt <= NumRed[t], pt++, ImageGraphicsList = Append[ImageGraphicsList, {Red, Disk[RedCoordsList[[pt]], radius]}]]; ImageGraphicsList = Append[ImageGraphicsList, DrawPie[2.5, 2.5, .4, FracRed[t]]]; Video = Append[Video, Graphics[ImageGraphicsList, ImageSize -> 100]];]; (* Slow the movie down at the beginning and end to make it easier to see *) Video = Join[ Table[Video[[1]], {i, 1, 3}], Table[Video[[2]], {i, 1, 3}], Table[Video[[3]], {i, 1, 3}], Table[Video[[4]], {i, 1, 3}], Table[Video[[5]], {i, 1, 3}], Table[Video[[6]], {i, 1, 2}], Table[Video[[7]], {i, 1, 2}], Table[Video[[8]], {i, 1, 2}], Table[Video[[9]], {i, 1, 2}], Table[Video[[10]], {i, 1, 2}], Video[[11 ;;]], Table[Video[[NumFrames]], {i, 1, 5}]]; (* Export *) Export["test.gif", Video, "DisplayDurations" -> {14}, "AnimationRepititions" -> Infinity]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 19:30, 25 March 2010 | ![]() | 100 × 169 (50 KB) | Aiyizo (talk | contribs) | Optimized animation, converted to 32 color mode |
23:13, 3 March 2010 | ![]() | 100 × 169 (477 KB) | Sbyrnes321 (talk | contribs) | longer simulation | |
07:43, 27 February 2010 | ![]() | 100 × 103 (172 KB) | Sbyrnes321 (talk | contribs) | {{Information |Description={{en|1=Simulation illustrating the Law of Large Numbers. Each frame, you flip a coin that is red on one side and blue on the other, and put a dot in the corresponding column. A pie chart notes the proportion of red and blue so f |
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