Hilbert_curve.ipynb

Hilbert_curve.ipynb

{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Hilbert Curve Drawing \n#### Order = 1, 2, 3 ... (4 dots, 16 dots, 64 dots ...)　　\n\n[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](http://colab.research.google.com/gist/mirrornerror/7c9f7d6cb3026dc4557eb7f600c07ad5/Hilbert_curve.ipynb) "
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-02-18T12:27:59.239566Z",
          "end_time": "2022-02-18T12:27:59.999513Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "from numpy import array, arange\nimport matplotlib.pyplot as plt\nfrom matplotlib import animation\nfrom IPython.display import HTML, display",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-02-18T12:28:01.181454Z",
          "end_time": "2022-02-18T12:28:01.225781Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Plot function\ndef Plot(X, Y, outline=False, num=False, dot=False):\n    N = int((len(X))**0.5)\n    fig = plt.figure(figsize=(8,8))\n    ax = fig.add_subplot(111)\n    ax.axis([0, N, 0, N])\n    \n    if outline == False:\n        ax.axis('off')\n    ax.plot(X, Y, color='tab:blue')\n    if num:\n        for i in range(len(X)):\n            ax.text(X[i]+0.02, Y[i]+0.02, s=str(i))\n    if dot:\n        ax.scatter(X, Y, color='tab:blue')\n    ax.grid()\n    plt.xticks(arange(0, N+1, max(1, N//4)))\n    plt.yticks(arange(0, N+1, max(1, N//4)))\n    plt.show()\n    plt.close()\n\n# Animation function\ndef Anim(X, Y, outline=False, save=False):\n    N = int((len(X))**0.5)\n    fig = plt.figure(figsize=(8,8))\n    ax = fig.add_subplot(111)\n    ax.axis([0, N, 0, N])\n    ax.grid()\n    plt.xticks(arange(0, N+1, max(1, N//4)))\n    plt.yticks(arange(0, N+1, max(1, N//4)))\n    if outline == False:\n        ax.axis('off')   \n    ims = []\n    for i in range(len(X) + 1):  \n        A = ax.plot(X[:i], Y[:i], color='tab:blue')\n        ims.append(A)\n    ani = animation.ArtistAnimation(fig,ims,interval=100)\n    if save:\n        ani.save('anim.gif', writer = 'pillow')  # writer='Imagemagick', 'ffmpeg', Windows for 'pillow'\n    #HTML(ani.to_html5_video())           \n    display(HTML(ani.to_jshtml()))\n    plt.close()",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-02-18T12:28:03.882607Z",
          "end_time": "2022-02-18T12:28:03.902515Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Hilbert curve function\ndef Hilbert(ORDER):                          # ORDER 1: 4 dots, ORDER 2: 16 dots, ORDER 3: 64 dots ...\n    N = 2**ORDER                             # the number of row or columns of the dots\n    X,Y = [], []                             # empty lists for X and Y coodinates outputs\n    for i in range(N * N):                   # iteration: the total number of the dots\n        U = [[0, 0], [0, 1], [1, 1], [1, 0]] # initial four dots coodinates: origin, up, right, down\n        px, py = 0.5, 0.5                    # starting coodinates (initial offsets)\n        for j in reversed(range(ORDER)):     # reversed iteration: j=2,1,0 when ORDER=3\n            ID = i // 4**j % 4               # index number depending on ORDER\n            L = 2**j                         # unit length under ORDER: L=4, 2, 1 when ORDER=3\n            if   ID == 0:\n                U[1], U[3] = U[3], U[1]      # swap 1st with 3rd dots when ID is 0\n            elif ID == 3:\n                U[0], U[2] = U[2], U[0]      # swap 0th with 2nd dots when ID is 3\n            px += U[ID][0] * L               # add each length depending on ORDER\n            py += U[ID][1] * L\n        X.append(px)                         # preserve (x, y) coodinates of the dots\n        Y.append(py)\n    return X, Y",
      "execution_count": 3,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Draw Hilvert Curve"
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-02-18T12:28:19.265054Z",
          "end_time": "2022-02-18T12:28:19.335951Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Draw Hilbert curve\nX, Y = Hilbert(4)   # argument: Order from 1 to n\nPlot(X, Y)  # arguments: X, Y, outline=False, num=False, dot=False\n#Anim(X, Y) # arguments: X, Y, outline=False, save=False",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 576x576 with 1 Axes>",
            "image/png": "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\n"
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      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
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