sync matplotlib

content/04-python-matplotlib/matplotlib-exercises.ipynb

@@ -14,8 +14,7 @@
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "%matplotlib inline"
+    "import numpy as np"
    ]
   },
   {
@@ -85,7 +84,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "outputs": [],
    "source": []
   },
@@ -97,13 +98,9 @@
     "\n",
     "For an angle $\\theta$ in the range $\\theta \\in [0, 2\\pi]$, the polar equations of a circle of radius $R$ are:\n",
     "\n",
-    "$$\n",
-    "x = R\\cos(\\theta)\n",
-    "$$\n",
+    "$$x = R\\cos(\\theta)$$\n",
     "\n",
-    "$$ \n",
-    "y = R\\sin(\\theta)\n",
-    "$$\n",
+    "$$y = R\\sin(\\theta)$$\n",
     "\n",
     "We want to draw a circle.   \n",
     "\n",
@@ -117,7 +114,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "outputs": [],
    "source": []
   },
@@ -139,7 +138,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "outputs": [],
    "source": []
   },
@@ -166,7 +167,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "outputs": [],
    "source": []
   },
@@ -176,7 +179,7 @@
    "source": [
     "## Q5: subplots\n",
     "\n",
-    "matplotlib has a number of ways to create multiple axes in a figure -- look at `plt.subplot()` (http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot)\n",
+    "matplotlib has a number of ways to create multiple axes in a figure -- look at `plt.subplots()` (http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot)\n",
     "\n",
     "Create an `x` array using NumPy with a number of points, spanning from $[0, 2\\pi]$.  \n",
     "\n",
@@ -185,62 +188,105 @@
     "* Define a new numpy array `f` initialized to a function of your choice.\n",
     "* Plot f in the top axes\n",
     "* Compute a numerical derivative of `f`,\n",
-    "\n",
     "   $$ f' = \\frac{f_{i+1} - f_i}{\\Delta x}$$\n",
-    "\n",
-    "and plot this in the middle axes\n",
+    "  and plot this in the middle axes\n",
     "* Do this again, this time on $f'$ to compute the second derivative and plot that in the bottom axes\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Q6: frequent words plotting\n",
+    "## Q6: Mandelbrot set\n",
+    "\n",
+    "The [Mandelbrot set](https://en.wikipedia.org/wiki/Mandelbrot_set) is defined such that $z_{k+1} = z_k^2 + c$\n",
+    "remains bounded, which is usually taken as $|z_{k+1}| \\le 2$\n",
+    "where $c$ is a complex number and we start with $z_0 = 0$\n",
+    "\n",
+    "We want to consider a range of $c$, as complex numbers $c = x + iy$,\n",
+    "where $-2 < x < 2$ and $-2 < y < 2$.\n",
     "\n",
-    "In this exercise, we will read the file with the transcription of _Star Trek TOS, Shore Leave_ and calculate the amount of time each word was found. We will then plot the 25 most frequent words and label the plot.\n",
+    "For each $c$, identify its position on a Cartesian grid as $(x,y)$ and \n",
+    "assign a value $N$ that is the number of iterations, $k$, required for $|z_{k+1}|$ to become greater than $2$.\n",
     "\n",
-    "### 6.1 Read the file and create the dictionaty {'word':count}\n",
+    "The plot of this function is called the Mandelbrot set.\n",
     "\n",
-    "   * Open the `shore_leave.txt`\n",
-    "   * Create the dictionary of the form {'word':count}, where `count` shows the amount of times the word was found in the text. Remember to get rid of the punctuation (\".\" and \",\") and to ensure that all words are lowercase"
+    "Here's a simple implementation that just does a fixed number of iterations and then colors points in Z depending on whether they satisfy $|z| \\le 2$.  \n",
+    "\n",
+    "Your task is to extend this to record the number of iterations it takes for each point in the Z-plane to violate that constraint,\n",
+    "and then plot that data -- it will show more structure\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
-    "f = open(\"shore_leave.txt\", \"r\")\n",
+    "N = 256\n",
+    "x = np.linspace(-2, 2, N)\n",
+    "y = np.linspace(-2, 2, N)\n",
     "\n",
-    "for line in f:\n",
-    "    pass"
+    "xv, yv = np.meshgrid(x, y, indexing=\"ij\")"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": 8,
    "metadata": {},
+   "outputs": [],
    "source": [
-    "### 2. Plot 25 most frequent words\n",
+    "c = xv + 1j*y\n",
+    "\n",
+    "z = np.zeros((N, N), dtype=np.complex128)\n",
     "\n",
-    "Plot a labelled bar chart of the most frequent 25 words with their frequencies."
+    "for i in range(10):\n",
+    "    z = z**2 + c\n",
+    "    \n",
+    "m = np.ones((N, N))\n",
+    "m[np.abs(z) <= 2] = 0.0"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 10,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.image.AxesImage at 0x7fd9934ba0e0>"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
-    "# your code here"
+    "fig, ax = plt.subplots()\n",
+    "ax.imshow(m)"
    ]
   },
   {
@@ -253,7 +299,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -267,7 +313,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.5"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,