programs/julia/dragon_curve.ipynb

dragon_curve.ipynb

{
  "cells": [
    {
      "metadata": {
        "scrolled": true,
        "trusted": false
      },
      "cell_type": "code",
      "source": "function duplicate!(xs, ys, last, mat)\n    center_x = xs[last]; center_y = ys[last]\n    for i in 1:last-1\n        dx = xs[last-i] - center_x\n        dy = ys[last-i] - center_y\n        xs[last+i] = mat[1,1]*dx + mat[1,2]*dy + center_x\n        ys[last+i] = mat[2,1]*dx + mat[2,2]*dy + center_y\n    end\nend",
      "execution_count": 1,
      "outputs": [
        {
          "data": {
            "text/plain": "duplicate! (generic function with 1 method)"
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": false
      },
      "cell_type": "code",
      "source": "function make_sin_table(n)\n    (k->sin(k*π/2n)).(0:n)\nend",
      "execution_count": 2,
      "outputs": [
        {
          "data": {
            "text/plain": "make_sin_table (generic function with 1 method)"
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": false
      },
      "cell_type": "code",
      "source": "using Plots\ngr(\n    legend=false\n    , xlims=(-100,50), ylims=(-50,100)\n    , xticks=nothing, yticks=nothing\n    , size=(500,500)\n)\nENV[\"PLOTS_TEST\"]=\"true\"\n\nmax_order = 10\nxs = Array{Float64, 1}(undef, 2 * 2^max_order + 1)\nys = Array{Float64, 1}(undef, 2 * 2^max_order + 1)\nxs[1] = 0; xs[2] = 1\nys[1] = 0; ys[2] = 0\n\nfp90 = 16\nsintbl = make_sin_table(fp90)\n\ndragon_unfolding = foldr(\n    append!,\n    (odr->(i->begin\n                len = 2^odr\n                duplicate!(xs, ys, len + 1,[\n                        sintbl[fp90-i+1] -sintbl[i+1]\n                        sintbl[i+1] sintbl[fp90-i+1]])\n                plot(getindex(xs, 1:2*len+1), getindex(ys, 1:2*len+1))\n              end).(1:fp90)).(0:max_order))\n\ndragon_folding = reverse(dragon_unfolding)\n@time @gif for plt = append!(\n        dragon_unfolding,\n        append!(\n            [\n                dragon_folding[1]\n                dragon_folding[1]\n                dragon_folding[1]],\n            dragon_folding))\n    plot(plt)\nend",
      "execution_count": 3,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": " 86"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": "┌ Info: Saved animation to \n│   fn = https://user-images.githubusercontent.com/35671444/77270986-ca49b380-6cf0-11ea-991c-8a1c4ff34ed4.gif\n└ @ Plots /home/brv00/.julia/packages/Plots/vTdnV/src/animation.jl:98\n"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": ".628516 seconds (6.22 M allocations: 322.864 MiB, 0.91% gc time)\n"
        },
        {
          "data": {
            "text/html": "<img src=\"https://user-images.githubusercontent.com/35671444/77270986-ca49b380-6cf0-11ea-991c-8a1c4ff34ed4.gif\" />",
            "text/plain": "Plots.AnimatedGif(\"https://user-images.githubusercontent.com/35671444/77270986-ca49b380-6cf0-11ea-991c-8a1c4ff34ed4.gif\")"
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    }
  ],
  "metadata": {
    "_draft": {
      "nbviewer_url": "https://gist.github.com/118ed8ecfed471fb41c7ff57b99878e2"
    },
    "gist": {
      "id": "118ed8ecfed471fb41c7ff57b99878e2",
      "data": {
        "description": "programs/julia/dragon_curve.ipynb",
        "public": true
      }
    },
    "kernelspec": {
      "name": "julia-1.3",
      "display_name": "Julia 1.3.1",
      "language": "julia"
    },
    "language_info": {
      "file_extension": ".jl",
      "name": "julia",
      "mimetype": "application/julia",
      "version": "1.3.1"
    }
  },
  "nbformat": 4,
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