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terasakisatoshi/hexagon_something.ipynb

Last active September 8, 2021 10:05
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hexagon_something.ipynb
{
"cells": [
{
"metadata": {
"ExecuteTime": {
"start_time": "2021-09-08T10:00:21.225Z",
"end_time": "2021-09-08T19:00:21.227000+09:00"
},
"trusted": true
},
"cell_type": "code",
"source": "using Plots\nusing StatsBase: sample",
"execution_count": 6,
"outputs": []
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2021-09-08T10:00:21.368Z",
"end_time": "2021-09-08T19:00:21.371000+09:00"
},
"trusted": true
},
"cell_type": "code",
"source": "using HTTP, JSON\nfunction display_tweet(link)\n api = \"https://publish.twitter.com/oembed?url=$link\"\n r = response = HTTP.request(\"GET\", api);\n j = JSON.parse(String(r.body))\n HTML(j[\"html\"])\nend",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": "display_tweet (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2021-09-08T10:00:21.640Z",
"end_time": "2021-09-08T19:00:21.875000+09:00"
},
"trusted": true
},
"cell_type": "code",
"source": "display_tweet(\"https://twitter.com/matthen2/status/1268808515574886407?s=20\")",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 8,
"data": {
"text/plain": "HTML{String}(\"<blockquote class=\\\"twitter-tweet\\\"><p lang=\\\"en\\\" dir=\\\"ltr\\\">a simple and random process that creates an intricate and structured fractal pattern. At each step, pick a random edge to form a triangle, and the next point is the center of the triangle. <a href=\\\"https://t.co/yLxmdZQCWY\\\">pic.twitter.com/yLxmdZQCWY</a></p>&mdash; Matt Henderson (@matthen2) <a href=\\\"https://twitter.com/matthen2/status/1268808515574886407?ref_src=twsrc%5Etfw\\\">June 5, 2020</a></blockquote>\\n<script async src=\\\"https://platform.twitter.com/widgets.js\\\" charset=\\\"utf-8\\\"></script>\\n\")",
"text/html": "<blockquote class=\"twitter-tweet\"><p lang=\"en\" dir=\"ltr\">a simple and random process that creates an intricate and structured fractal pattern. At each step, pick a random edge to form a triangle, and the next point is the center of the triangle. <a href=\"https://t.co/yLxmdZQCWY\">pic.twitter.com/yLxmdZQCWY</a></p>&mdash; Matt Henderson (@matthen2) <a href=\"https://twitter.com/matthen2/status/1268808515574886407?ref_src=twsrc%5Etfw\">June 5, 2020</a></blockquote>\n<script async src=\"https://platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-09-08T18:28:00.354000+09:00",
"start_time": "2021-09-08T09:28:00.353Z"
}
},
"cell_type": "markdown",
"source": "using StatsPlots\nusing Distributions: sample"
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2021-09-08T10:00:23.778Z",
"end_time": "2021-09-08T19:00:50.865000+09:00"
},
"trusted": true
},
"cell_type": "code",
"source": "function create_anim(N;niter=500, disp=true)\n r = 4\n pxs = []\n pys = []\n\n for θ ∈ range(π/2, stop=(2π+π/2), length=(N+1))\n push!(pxs, r * cos(θ))\n push!(pys, r * sin(θ))\n end\n \n p = plot(aspect_ratio=:equal, legend=false, axis=false, grid=false, ticks=false)\n plot!(p, pxs, pys, markershape=:auto)\n\n θ₀ = 2π*rand()\n\n inner_r = cos(π/N) * r * rand()\n\n # 内接円で適当に選ぶ\n px0 = inner_r * cos(θ₀)\n py0 = inner_r * sin(θ₀)\n\n scatter!(p, [px0], [py0], color=:red)\n \n disp_it = disp && isdefined(Main, :IJulia)\n \n anim = @animate for t ∈ 1:niter\n disp_it && IJulia.clear_output(true)\n scatter!(p, [px0], [py0], color=:black, msize=2)\n disp_it && display(p)\n # select two points\n i = sample(1:N)\n px1 = pxs[i]\n py1 = pys[i]\n px2 = pxs[i+1]\n py2 = pys[i+1]\n \n # centroid\n cx = (px0 + px1 + px2)/3\n cy = (py0 + py1 + py2)/3\n\n # update\n px0 = cx\n py0 = cy\n end\n anim\nend\n\nanim = create_anim(6, niter=500, disp=false)\ngif(anim)",
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": "┌ Info: Saved animation to \n│ fn = /Users/terasaki/tmp/tmp.gif\n└ @ Plots /Users/terasaki/.julia/packages/Plots/Di0Qb/src/animation.jl:114\n",
"name": "stderr"
},
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": "Plots.AnimatedGif(\"/Users/terasaki/tmp/tmp.gif\")",
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\" />"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"start_time": "2021-09-08T10:04:37.611Z",
"end_time": "2021-09-08T19:04:38.751000+09:00"
},
"trusted": true
},
"cell_type": "code",
"source": "function display_result(N;niter=500, disp=true)\n r = 4\n pxs = []\n pys = []\n\n for θ ∈ range(π/2, stop=(2π+π/2), length=(N+1))\n push!(pxs, r * cos(θ))\n push!(pys, r * sin(θ))\n end\n \n p = plot(aspect_ratio=:equal, legend=false, axis=false, grid=false, ticks=false)\n plot!(p, pxs, pys, markershape=:auto)\n\n θ₀ = 2π*rand()\n\n inner_r = cos(π/N) * r * rand()\n\n # 内接円で適当に選ぶ\n px0 = inner_r * cos(θ₀)\n py0 = inner_r * sin(θ₀)\n \n rx = [px0]\n ry = [py0]\n \n for t ∈ 1:niter\n # select two points\n i = sample(1:N)\n px1 = pxs[i]\n py1 = pys[i]\n \n px2 = pxs[i+1]\n py2 = pys[i+1]\n \n # centroid\n cx = (px0 + px1 + px2)/3\n cy = (py0 + py1 + py2)/3\n push!(rx, cx)\n push!(ry, cy)\n # update\n px0 = cx\n py0 = cy\n end\n scatter!(p, rx, ry, msize=1, legend=false, color=:black)\n p\nend\n\ndisplay_result(5, niter=50000, disp=false)",
"execution_count": 28,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 28,
"data": {
"image/png": 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