notebook/Fibonacci.ipynb

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   "source": [
    "# Fibonacci sequence\n",
    "_Gilbert François Duivesteijn_\n",
    "\n",
    "\n",
    "## Abstract\n",
    "\n",
    "This notebook explores the Fibonacci numbers in more depth, and shows that the sequence is related to the golden ratio. More over, the Fibonacci numbers can be exteded from a discrete series of natural numbers, to a continuous function in the complex plane. The latter shows that all the discrete series are a subset of the generic continuous function in the complex plane."
   ]
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   "id": "37def897-35af-4e2e-b543-9bb74552252d",
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d2e7b569-281e-42c7-b1bc-dc67e6bfd205",
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   "outputs": [],
   "source": [
    "def plot(x):\n",
    "    \"\"\"\n",
    "    Plots the sequence on the 1D number line.\n",
    "    \n",
    "    Parameter\n",
    "    ---------\n",
    "    x: np.ndarray\n",
    "        Sequence of numbers\n",
    "    \"\"\"\n",
    "    plt.figure(figsize=(9,0.5))\n",
    "    plt.scatter(x=x, y=np.zeros_like(x), marker='o', color=\"black\")\n",
    "    plt.xlim([x.min()-1, x.max()+1])\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.tick_params(axis='y', which='both', left=False, right=False, labelleft=False)\n",
    "    ax = plt.gca()\n",
    "    ax.spines['left'].set_color('none')\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['bottom'].set_position('zero')\n",
    "    ax.spines['top'].set_color('none')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3694335f-1907-4750-9043-c086a9a968ec",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Fibonacci in $\\mathbb{N}$\n",
    "\n",
    "The Fibonacci numbers may be defined by the recurrence relation:\n",
    "\n",
    "\\begin{align}\n",
    "F_0 &= 0 \\\\\n",
    "F_1 &= 1 \\\\\n",
    "F_i &= F_{i-2} + F_{i-1} \\qquad i \\in \\mathbb{N}, i \\geq 2\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f3169330-c526-4620-9bea-672ffd413fbc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def fibonacci(F0, F1, n, dtype=int):\n",
    "    \"\"\"\n",
    "    Computes Fibonacci sequence in positive direction.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    F0: int|float\n",
    "        First starting number\n",
    "    F1: int|float\n",
    "        Second starting number\n",
    "    n: int\n",
    "        number of digits in the sequence.\n",
    "    dtype: dtype (optional)\n",
    "        int or float\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    np.ndarray\n",
    "        Sequence\n",
    "    \"\"\"\n",
    "    seq = np.zeros(shape=(n,), dtype=dtype)\n",
    "    seq[0] = F0\n",
    "    seq[1] = F1\n",
    "    for i in range(2, n):\n",
    "        seq[i] = seq[i-2] + seq[i-1]\n",
    "    return np.array(seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b5dec64c-0e78-4669-a703-1938dd08cf05",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  1  2  3  5  8 13 21 34]\n"
     ]
    },
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       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "seq = fibonacci(0, 1, 10)\n",
    "\n",
    "plot(seq)\n",
    "print(seq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf1c8fe6-c714-47ca-b5ef-8411727db408",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Fibonacci in $\\mathbb{Z}$\n",
    "\n",
    "The Fibonacci numbers may be defined by the recurrence relation:\n",
    "\n",
    "\\begin{align}\n",
    "F_{i-2} &= -F_{i-1} + F_{i} \\qquad i \\in \\mathbb{Z}\n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "91cc98f8-2032-49a5-a7eb-9063f7722b41",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def fibonacci_rev(F0, F1, n, dtype=int):\n",
    "    \"\"\"\n",
    "    Computes Fibonacci sequence in negative direction.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    F0: int|float\n",
    "        First starting number\n",
    "    F1: int|float\n",
    "        Second starting number\n",
    "    n: int\n",
    "        number of digits in the sequence.\n",
    "    dtype: dtype (optional)\n",
    "        int or float\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    np.ndarray\n",
    "        Sequence\n",
    "    \"\"\"\n",
    "\n",
    "    seq = np.zeros(shape=(n,), dtype=dtype)\n",
    "    seq[n-2] = F0\n",
    "    seq[n-1] = F1\n",
    "    for i in range(n-1, 1, -1):\n",
    "        seq[i-2] = - seq[i-1] + seq[i]\n",
    "    return np.array(seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c17749df-24d7-4499-9ecb-b594f4b9b418",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-21  13  -8   5  -3   2  -1   1   0   1]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1f9270e424ca433786463fb6a705b881",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA4QAAAAyCAYAAAAENRXOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAL+UlEQVR4nO3df0zU9R8H8OdxdQcoIIR6hyCcVJQt0WxcWtckmZczt/5hrh+OmmsVlKtTIipELYWBica8sD/C/urHxmqrWcsxt2hetNGo6aYTBsPwDmslFzY5Pd7fPxz39QL5+YH3h8/7+dhu8z738ePz4+v9/sDrPnefj0kIIUBERERERETKiZEdgIiIiIiIiORgQ0hERERERKQoNoRERERERESKYkNIRERERESkKDaEREREREREimJDSEREREREpCg2hERERERERIpiQ0hERERERKQoNoRERERERESKYkNIRERERESkKDaEREREREREimJDSEREREREpCg2hERERERERIpiQ0hERERERKQoNoRERERERESKYkNIRERERESkKDaEREREREREimJDSEREREREpCg2hERERERERIq6TXYA0odwOIyWlhb4/X7Y7Xa4XC6YzWbZsYhoBnC+y6fXGmidS8vthUIheL1edHZ2Ijs7G8XFxbBYLLrIpmeq7CfJx7E2hwlSXlNTk0hPTxcAIo/09HTR1NQkOxoRaYzzXT691kDrXFpur7S0VJjN5qhtmc1mUVpaKj2bnqmynyQfx9rcxoZQcU1NTcJkMkVNYADCZDIJk8nEiUxkIJzv8um1Blrn0nJ7paWlI7Zz82OyTaFea6A1VfaT5ONYm/tMQggx3bOMNDeFw2FkZWXh999/H/V1k8mE9PR0dHV18ZQ/0RzH+S6fXmugdS4ttxcKhRAfH49wOHzLdcxmM/79998JfXxUrzXQmir7SfJxrBkDv0M4xwkh8M8//0zp77a0tNxyAg9v+8KFC/juu+/gcrmmGpGIdIDzXT691kDrXFpuz+v1jtkMAjd+IT148CCKi4tnNZueqbKfJN9sjLWEhASYTKapRqQJ4BnCOS4YDCIpKUl2DCIiIiIizfX39yMxMVF2DENjQzjHTfcM4RNPPDHuet98882k39UJBoPIyMjAhQsXOIklYQ3k01MNZnK+6xlrMD6tc2m5Pa/Xi/Ly8nG3VVVVNeEzhHqsgdZU2c+5RE/HIi3NxljjGcKZx4ZQYcOf++7t7cVow2A6n/sePnPJd3XkYQ3k01MNZnK+6xlrMPu5tNzeTH2HUG810Joq+zmX6OlYpCWONWPgjekVZjabcfjwYQAY8c7L8PNDhw5xAhMZAOe7fHqtgda5tNyexWKBx+MZcx2PxzPh+xHqtQZaU2U/ST6ONYOYrcuZkn6Ndu+YjIyMaV0muL+/XwAQ/f39GialyWAN5NNjDWZivusZayAvl5bbm437EOqhBlpTZT/nAj0ei7TEsTa38SOjBODGKf+Wlhb4/X7Y7Xa4XK5pvZszODiIqqoqlJeXw2q1apiUJoo1kE+vNdB6vusZayA3VzgcRnNzM44ePYoXX3wR69evn/L2QqEQvF4vOjs7kZ2djeLi4gmfGbxVNj3WQGta1oCmTq/HIi2pMqeMiA0hERERERGRovgdQiIiIiIiIkWxISQiIiIiIlIUG0IiIiIiIiJFsSEkIiIiIiJSFBtC0lR3dze2bdsGh8OBuLg4ZGdno7KyEqFQKGq93377DS6XC7GxscjIyEBNTY2kxMa0b98+rF27FvHx8ViwYMGo65hMphGPzz77bHaDGthEatDT04NNmzYhPj4eixYtQmlpKa5fvz67QRWSlZU1YsxXV1fLjmVoR44cQVZWFmJjY+F0OvHzzz/LjqSM3bt3jxjv99xzj+xYhvbDDz9g8+bNSEtLg8lkwldffRX1uhACu3btgt1uR1xcHAoKCnD+/Hk5YYluwoaQNHX27FkMDQ3h6NGjOHPmDOrq6tDQ0IC33norsk4wGMSGDRuQmZmJtrY21NbWYvfu3fjoo48kJjeWUCiEwsJCvPzyy2Ou19jYCL/fH3k8+eSTsxNQAePVIBwOY9OmTQiFQjh16hQ++eQTHDt2DLt27ZrlpGrZu3dv1Jh/9dVXZUcyrM8//xwejweVlZX45ZdfkJubC7fbjUuXLsmOpoz77rsvarz/+OOPsiMZ2pUrV5Cbm4sjR46M+npNTQ0++OADNDQ0oLW1FfPmzYPb7cbVq1dnOSnRf0i9CyIpoaamRjgcjshzr9crkpOTxeDgYGRZWVmZyMnJkRHP0BobG0VSUtKorwEQX3755azmUdGtanD8+HERExMjAoFAZNmHH34oEhMTo+YGaSczM1PU1dXJjqGMvLw8UVJSEnkeDodFWlqaqKqqkphKHZWVlSI3N1d2DGX992fs0NCQsNlsora2NrLs8uXLwmq1ik8//VRCQqL/4xlCmnH9/f1ISUmJPPf5fHj00Uejbijsdrtx7tw5/P333zIiKqukpASpqanIy8vDxx9/DMHbks4an8+H+++/H4sXL44sc7vdCAaDOHPmjMRkxlZdXY077rgDq1atQm1tLT+iO0NCoRDa2tpQUFAQWRYTE4OCggL4fD6JydRy/vx5pKWlYdmyZXjmmWfQ09MjO5Kyurq6EAgEouZEUlISnE4n5wRJd5vsAGRsHR0dqK+vx4EDByLLAoEAHA5H1HrDvxQHAgEkJyfPakZV7d27F4899hji4+Px/fffo7i4GAMDA9i+fbvsaEoIBAJRzSAQPQ9Ie9u3b8cDDzyAlJQUnDp1CuXl5fD7/Th48KDsaIbz559/IhwOjzrGz549KymVWpxOJ44dO4acnBz4/X7s2bMHLpcLp0+fRkJCgux4yhk+ro82J3jMJ9l4hpAm5M033xz1IiQ3P/77Q763txePP/44CgsL8cILL0hKbhxTqcFYKioq8PDDD2PVqlUoKyvDG2+8gdra2hncg7lP6xrQ9E2mJh6PB+vWrcOKFSvw0ksv4f3330d9fT0GBwcl7wWR9jZu3IjCwkKsWLECbrcbx48fx+XLl/HFF1/IjkZEOsMzhDQhO3bswHPPPTfmOsuWLYv8+eLFi8jPz8fatWtHXCzGZrOhr68vatnwc5vNpk1gA5psDSbL6XTi3XffxeDgIKxW65S3Y2Ra1sBms4244iLnweRNpyZOpxPXr19Hd3c3cnJyZiCdulJTU2E2m0c91nN8y7FgwQLcfffd6OjokB1FScPjvq+vD3a7PbK8r68PK1eulJSK6AY2hDQhCxcuxMKFCye0bm9vL/Lz87F69Wo0NjYiJib6RPSaNWvw9ttv49q1a7j99tsBACdOnEBOTg4/LjqGydRgKtrb25GcnMxmcAxa1mDNmjXYt28fLl26hEWLFgG4MQ8SExOxfPlyTf4NFUynJu3t7YiJiYn8/5N2LBYLVq9ejebm5sjVi4eGhtDc3IxXXnlFbjhFDQwMoLOzE1u3bpUdRUkOhwM2mw3Nzc2RBjAYDKK1tXXcK4ITzTQ2hKSp3t5erFu3DpmZmThw4AD++OOPyGvD7449/fTT2LNnD7Zt24aysjKcPn0ahw8fRl1dnazYhtPT04O//voLPT09CIfDaG9vBwDceeedmD9/Pr7++mv09fXhoYceQmxsLE6cOIH9+/dj586dcoMbyHg12LBhA5YvX46tW7eipqYGgUAA77zzDkpKStiUzwCfz4fW1lbk5+cjISEBPp8Pr7/+Op599lm+ETVDPB4PioqK8OCDDyIvLw+HDh3ClStX8Pzzz8uOpoSdO3di8+bNyMzMxMWLF1FZWQmz2YynnnpKdjTDGhgYiDoD29XVhfb2dqSkpGDp0qV47bXX8N577+Guu+6Cw+FARUUF0tLSeMsnkk/2ZU7JWBobGwWAUR83+/XXX8UjjzwirFarWLJkiaiurpaU2JiKiopGrcHJkyeFEEJ8++23YuXKlWL+/Pli3rx5Ijc3VzQ0NIhwOCw3uIGMVwMhhOju7hYbN24UcXFxIjU1VezYsUNcu3ZNXmgDa2trE06nUyQlJYnY2Fhx7733iv3794urV6/KjmZo9fX1YunSpcJisYi8vDzx008/yY6kjC1btgi73S4sFotYsmSJ2LJli+jo6JAdy9BOnjw56nG/qKhICHHj1hMVFRVi8eLFwmq1ivXr14tz587JDU0khDAJwevMExERERERqYhXGSUiIiIiIlIUG0IiIiIiIiJFsSEkIiIiIiJS1P8A8NsdRWps/0YAAAAASUVORK5CYII=' width=900.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq = fibonacci_rev(0, 1, 10)\n",
    "\n",
    "plot(seq)\n",
    "print(seq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d330b25-917d-4e7b-a3d0-633b264e81d4",
   "metadata": {},
   "source": [
    "## Fibonacci in $\\mathbb{R}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bf749004-d2d8-4a3b-be60-f4a496b08807",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.2   3.3   5.5   8.8  14.3  23.1  37.4  60.5  97.9 158.4]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e9c1cc3277ff45919e977d128f2b9643",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=900.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq = fibonacci(2.2, 3.3, 10, dtype=float)\n",
    "\n",
    "plot(seq)\n",
    "print(seq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ff553d1-664b-4dc0-906d-3c43f94dbe15",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Golden ratio\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{F_{i}}{F_{i-1}} &= \\frac{F_{i-1}}{F_{i-2}} = \\phi\\\\\n",
    "\\end{align}\n",
    "\n",
    "with \n",
    "\n",
    "\\begin{align}\n",
    "F_i &= F_{i-2} + F_{i-1}\n",
    "\\end{align}\n",
    "\n",
    "we can write\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{F_{i-1}+F_{i-2}}{F_{i-1}} &= \\frac{F_{i-1}}{F_{i-2}} \\\\\n",
    "1+\\frac{F_{i-2}}{F_{i-1}} &= \\frac{F_{i-1}}{F_{i-2}} \\\\\n",
    "\\end{align}\n",
    "\n",
    "Recall that $\\frac{F_{i-1}}{F_{i-2}}=\\phi$, the equation becomes\n",
    "\\begin{align}\n",
    "1 + \\frac{1}{\\phi} = \\phi\n",
    "\\end{align}\n",
    "\n",
    "There are many methods to obtain the solution for $\\phi$. Here we will use the quadratic formula. \n",
    "\n",
    "Multiply both sides with $\\phi$:\n",
    "\\begin{align}\n",
    "\\phi + 1 = \\phi^2\n",
    "\\end{align}\n",
    "\n",
    "Rearrange to\n",
    "\\begin{align}\n",
    "\\phi^2 - \\phi -1 = 0\n",
    "\\end{align}\n",
    "\n",
    "and use the quadratic formula to solve $\\phi$:\n",
    "\\begin{align}\n",
    "\\phi = \\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}\n",
    "\\end{align}\n",
    "\n",
    "With $a=1$, $b=-1$ and $c=-1$:\n",
    "\\begin{align}\n",
    "\\phi = \\frac{1}{2} \\pm \\frac{\\sqrt{5}}{2}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "In positive direction:\n",
    "\\begin{align}\n",
    "\\phi &= \\lim_{i \\rightarrow \\infty} \\frac{F_{i+1}}{F_i} \\qquad i \\in [0, \\infty) \\\\\n",
    "     &= 1.618033988749895\\cdots\n",
    "\\end{align}\n",
    "\n",
    "In negative direction:\n",
    "\\begin{align}\n",
    "\\psi &= \\lim_{i \\rightarrow -\\infty} \\frac{F_{i+1}}{F_{i}} \\qquad i \\in (-\\infty, 0] \\\\\n",
    "     &= -0.6180339887498948\\cdots \\\\\n",
    "     &= -\\frac{1}{\\phi}\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fcbc33c6-8100-44bb-ba27-83ce30e13bd8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bff54bdf05574ec98b5fa8f551adc774",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = (1 + np.sqrt(5))/2\n",
    "psi = (1 - np.sqrt(5))/2\n",
    "\n",
    "seq_pos = fibonacci(1, 1, 9)\n",
    "ratio_pos = seq_pos[1:]/seq_pos[:-1] \n",
    "\n",
    "seq_neg = fibonacci_rev(1, 0, 9)\n",
    "ratio_neg = seq_neg[1:]/(seq_neg[:-1]) \n",
    "\n",
    "fig, axs = plt.subplots(2, 1)\n",
    "axs[0].plot(seq_pos[1:], ratio_pos, marker='o', color=\"black\")\n",
    "axs[0].plot(seq_pos[1:], np.ones_like(seq_pos[1:])*phi, \"-.\", color=\"red\", label=\"$\\phi$\")\n",
    "axs[1].plot(seq_neg[1:], ratio_neg, marker='o', color=\"black\")\n",
    "axs[1].plot(seq_neg[1:], np.ones_like(seq_neg[1:])*psi, \"-.\", color=\"red\", label=\"$\\psi$\")\n",
    "axs[0].legend()\n",
    "axs[1].legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc4ef4cc-eb71-4ab2-99df-8a09048a194e",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Fibonacci in $\\mathbb{C}$\n",
    "\n",
    "With help of Binet's formula\n",
    "\\begin{align}\n",
    "F_i &= \\frac{\\phi^i - \\psi^i}{\\phi - \\psi} \\\\\n",
    "\\end{align}\n",
    "\n",
    "we can find any $i$-th Fibonacci number. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0f662b9c-9e46-49c9-8c1c-9600a26249aa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "phi = (1 + np.sqrt(5))/2\n",
    "psi = (1 - np.sqrt(5))/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1dc59584-cfba-4224-8b77-326ff3efd7e8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def binet(i):\n",
    "    \"\"\"\n",
    "    Binet's function\n",
    "    \n",
    "    Parameter\n",
    "    ---------\n",
    "    i: int|float\n",
    "        Requesting i-th digit in the fibonacci sequence.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    int|float\n",
    "        i_th Fibonacci number\n",
    "    \"\"\"\n",
    "    Fi = (np.power(phi, i) - np.power(psi,i))/(phi - psi)\n",
    "    return Fi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1825282-37cb-44cb-921d-2befe6dd1c03",
   "metadata": {},
   "source": [
    "Example: Let's find the 7th Fibonacci number with Binet's formula:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dae1795e-d697-483d-be3d-b8e9be43d96a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.000000000000002"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binet(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db031728-437f-452e-872f-266fba7ce001",
   "metadata": {},
   "source": [
    "However, this only works for $i \\in \\mathbb{Z}$, not for $i \\in \\mathbb{R}$. Recall that $\\psi = \\frac{-1}{\\phi}$ and computing the power of a number with a fractional exponent, is effectively taking a square root of a number. The square root of a negative number does not exist, unless we allow complex numbers, where \n",
    "\n",
    "\\begin{align}\n",
    "j^2 &= -1\\\\\n",
    "j &= \\sqrt{-1}\n",
    "\\end{align}\n",
    "\n",
    "Let's compute the 1.1th Fibonacci number. To make it work in Numpy, we have to fill in a complex number for $n$, where $n = 1.1 + 0j$ or $\\Re{(n)} = 1.1, \\Im{(n)}=0$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c09a97c0-37fe-4649-b782-c8dfa903e38a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.009794706934108+0.0813974796159386j)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binet(1.1+0j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41af7284-26a1-4562-ac58-e0f97c3c8279",
   "metadata": {},
   "source": [
    "---\n",
    "Find _all_ values of $F_i$, $i \\in [0, \\infty)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "124106b4-a2d9-426e-9fdb-6f10bf504481",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b02b2ad94d36408ca4ec179e78c12e63",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 6, 101)\n",
    "x = x + 0j\n",
    "y = binet(x)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(np.real(y), np.imag(y), color=\"black\")\n",
    "ax = plt.gca()\n",
    "ax.spines['left'].set_position('zero')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('zero')\n",
    "ax.spines['top'].set_color('none')\n",
    "plt.xlabel(\"$\\Re$\")\n",
    "plt.ylabel(\"$\\Im$\")\n",
    "plt.title(\"Continuous Fibonacci function, $n \\in [0, \\infty), F_i \\in \\mathbb{C}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee4b644f-93f7-42ea-a035-5bee1b0ff7ad",
   "metadata": {},
   "source": [
    "Note that on the $\\Re$ axis, we find all the Fibonacci numbers in $\\mathbb{N}$, as shown in section \"Fibonacci in $\\mathbb{N}$\", namely $0, 1, 1, 2, 3, 5, 8, \\cdots$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd804ecb-ebcb-447c-8136-ab57b84e2bd8",
   "metadata": {},
   "source": [
    "---\n",
    "Find _all_ values of $F_i$, $i \\in (-\\infty, 0]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01ed0520-c485-493a-bf87-c277afddf3cb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b540fbbc750945978c5160738aea323b",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-7, 0, 501)\n",
    "x = x + 0j\n",
    "y = binet(x)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(np.real(y), np.imag(y), color=\"black\")\n",
    "ax = plt.gca()\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.spines['left'].set_position('zero')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('zero')\n",
    "ax.spines['top'].set_color('none')\n",
    "plt.xlabel(\"$\\Re$\")\n",
    "plt.ylabel(\"$\\Im$\")\n",
    "plt.title(\"Continuous Fibonacci function, $i \\in (-\\infty, 0], F_i \\in \\mathbb{C}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "982a99c3-c8c2-4953-84b4-7bf5f3147dc6",
   "metadata": {},
   "source": [
    "Note that on the $\\Re$ axis, we find all the Fibonacci numbers in $\\mathbb{Z}$, as shown in section \"Fibonacci in $\\mathbb{Z}$\", namely $0, 1, -1, 2, -3, 5, -8, 13, \\cdots$."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}