ssugiyama · May 31, 2017 15:37
diff --git a/the_power_of_i.ipynb b/the_power_of_i.ipynb
 {
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization of $(x+y\\mathrm{i})^\\mathrm{i}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import ticker\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "%matplotlib inline \n",
    "\n",
    "x = np.arange(-3, 3, 0.01)\n",
    "y = np.arange(-3, 3, 0.01)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = (X+ Y*1j)**1j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## absolute values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k/aDJbwMftB3j/ZTHEWmkvXv3xj65nQe8DGyndWX3dTM7A7gbGABGgKvd/cDYG8xsFjDN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\nWja6Umw+sgwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105cee908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(X,Y,np.abs(Z), locator=ticker.LogLocator(base=2))\n",
    "formatter = ticker.LogFormatter(2, labelOnlyBase=False) \n",
    "plt.colorbar(format=formatter)\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S99N99903c31ZaQSWg5g7RUy0nuKjAMuJOke9af3ESQGWo6mpKXWUGtI6iZcCrADqMPWg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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a07f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(X,Y,np.angle(Z))\n",
    "plt.colorbar()\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Visualization of $(x+y\\mathrm{i})^\\mathrm{i}$"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"from matplotlib import pyplot as plt\n",
	"from matplotlib import ticker\n",
	"import numpy as np\n",
	"import seaborn as sns\n",
	"%matplotlib inline \n",
	"\n",
	"x = np.arange(-3, 3, 0.01)\n",
	"y = np.arange(-3, 3, 0.01)\n",
	"X, Y = np.meshgrid(x, y)\n",
	"Z = (X+ Y1j)*1j"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## absolute values"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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k/aDJbwMftB3j/ZTHEWmkvXv3xj65nQe8DGyndWX3dTM7A7gbGABGgKvd/cDYG8xsFjDN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\nWja6Umw+sgwAAAAASUVORK5CYII=\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x105cee908>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"plt.contourf(X,Y,np.abs(Z), locator=ticker.LogLocator(base=2))\n",
	"formatter = ticker.LogFormatter(2, labelOnlyBase=False) \n",
	"plt.colorbar(format=formatter)\n",
	"plt.gca().set_aspect('equal')\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## angles"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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S99N99903c31ZaQSWg5g7RUy0nuKjAMuJOke9af3ESQGWo6mpKXWUGtI6iZcCrADqMPWg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\nQmCC\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x108a07f60>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"plt.contourf(X,Y,np.angle(Z))\n",
	"plt.colorbar()\n",
	"plt.gca().set_aspect('equal')\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.6.1"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}