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@mandel59
Last active November 26, 2022 10:24
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√2の肩に無限に√2を乗せたらなぜ2になるのか、その図解
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# √2の肩に無限に√2を乗せたらなぜ2になるのか、その図解\n",
"\n",
"ここでは、YouTubeの動画[「√2の肩に無限に√2を乗せたらなぜ2になるのか」](https://www.youtube.com/watch?v=LABUpfm-rF0)で取り上げられている問題を考えてみたい。\n",
"\n",
"この記事ではまず、「$\\sqrt{2}$の肩に無限に$\\sqrt{2}$を乗せた」式の意味を、[**テトレーション**](https://ja.wikipedia.org/wiki/%E3%83%86%E3%83%88%E3%83%AC%E3%83%BC%E3%82%B7%E3%83%A7%E3%83%B3)と極限を使って簡潔に表現できることを説明する。次に、Pythonを使ったプログラムで、テトレーションを実際に計算し、その結果を[**クモの巣図法**](https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%A2%E3%81%AE%E5%B7%A3%E5%9B%B3%E6%B3%95)を使って可視化する。\n",
"\n",
"## テトレーションの導入\n",
"\n",
"同じ数の足し算を繰り返したら掛け算になり、同じ数の掛け算を繰り返したら冪乗になる。それと同様に、冪乗を繰り返した演算が存在し、**テトレーション**と呼ばれている。数$b$の冪乗を$n$回繰り返した演算を $b \\uparrow \\uparrow n$ という記号で表記し、**$b$の第$n$テトレーション**と読む。$b \\uparrow \\uparrow n$ は、形式的には次のように帰納的に定義できる:\n",
"\n",
"$$\n",
" {b \\uparrow \\uparrow n} = \\begin{cases}\n",
" 1 & \\mathrm{if} \\; n = 0 \\\\\n",
" b^{(b \\uparrow \\uparrow (n - 1))} & \\mathrm{if} \\; n \\geq 0\n",
" \\end{cases}\n",
"$$\n",
"\n",
"具体的には、\n",
"\n",
"$${b \\uparrow \\uparrow 0} = 1$$\n",
"$${b \\uparrow \\uparrow 1} = {b^{\\left(b \\uparrow \\uparrow 0\\right)}} = b$$\n",
"$${b \\uparrow \\uparrow 2} = {b^{\\left(b \\uparrow \\uparrow 1\\right)}} = {b^b}$$\n",
"$${b \\uparrow \\uparrow 3} = b^{{\\left(b \\uparrow \\uparrow 2\\right)}} = {b^{b^b}}$$\n",
"$${b \\uparrow \\uparrow 4} = b^{{\\left(b \\uparrow \\uparrow 3\\right)}} = {b^{b^{b^b}}}$$\n",
"\n",
"のようになる。テトレーション $b \\uparrow \\uparrow n$ の各項について、$b$をテトレーションの**底**、$n$をテトレーションの**高さ**と呼ぶ。\n",
"\n",
"テトレーションという演算を導入すれば、「$\\sqrt{2}$の肩に無限に$\\sqrt{2}$を乗せた」式は、数列 $\\left( \\sqrt{2} \\uparrow \\uparrow n \\right)_{n = 0, 1, 2, \\cdots}$ の極限として\n",
"\n",
"$$\n",
" \\sqrt{2} ^ {\\sqrt{2} ^ {\\sqrt{2} ^ ⋰}} = \\lim_{n \\rightarrow \\infty} \\left ( \\sqrt{2} \\uparrow \\uparrow n \\right )\n",
"$$\n",
"\n",
"のように定義できる。\n",
"\n",
"Pythonを使って、数列 $\\left( \\sqrt{2} \\uparrow \\uparrow n \\right)_{n = 0, 1, 2, \\cdots}$ の各項の値を計算をしてみよう。関数 $f(x) = b^x$ を使って差分方程式 $a_{n+1} = f(a_n)$ 、初期値 $a_0 = 1$ を考えた時、テトレーションの定義から自明に $a_{n} = b \\uparrow \\uparrow n$ となる。この差分方程式を使って、計算するプログラムを書く。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1. 1.41421356 1.63252692 1.76083956 1.84091087 1.8927127\n",
" 1.9269997 1.95003477 1.96566489 1.97634175 1.9836684 1.98871177\n",
" 1.99219088 1.99459445 1.99625667 1.997407 1.99820348 1.99875513\n",
" 1.99913731 1.99940212 1.99958562]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"# テトレーションの底\n",
"b = np.sqrt(2)\n",
"\n",
"# 繰り返し回数\n",
"N = 20\n",
"\n",
"# 差分方程式の関数\n",
"def f(x):\n",
" return np.power(b, x)\n",
"# 初期値\n",
"a0 = 1\n",
"\n",
"def calculate_a(f, a0):\n",
" \"\"\"差分方程式と初期値から数列 (a_n)_{n=0, 1, ..., N} を計算する\"\"\"\n",
" a = np.empty(N + 1)\n",
" # 初期値\n",
" a[0] = a0\n",
" for n in range(0, N):\n",
" # 差分方程式\n",
" a[n + 1] = f(a[n])\n",
" return a\n",
"\n",
"a = calculate_a(f, a0)\n",
"\n",
"print(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## クモの巣図法\n",
"\n",
"差分方程式 $a_{n+1} = f(a_n)$ 、初期値 $a_0$ について、 $n$ を増やすにつれ、値はどのように変わっていくのかを、**クモの巣図法**を使って図示することができる。\n",
"\n",
"\n",
"クモの巣図法は $y = f(x)$ と $y = x$ の間で垂直・水平な線を交互に引いていくことで描くことができる。"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.4142135623730951 [1. 1.41421356 1.63252692 1.76083956 1.84091087 1.8927127\n",
" 1.9269997 1.95003477 1.96566489 1.97634175 1.9836684 1.98871177\n",
" 1.99219088 1.99459445 1.99625667 1.997407 1.99820348 1.99875513\n",
" 1.99913731 1.99940212 1.99958562]\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# x軸は0≦x≦6の範囲で、等間隔に1000点で計算する。\n",
"x = np.linspace(0, 6, 1000)\n",
"\n",
"def cobweb(a):\n",
" \"\"\"クモの巣図法でプロットする点を計算する\"\"\"\n",
" # 最初の点は座標 (a[0], 0)\n",
" p0 = (a[0], 0)\n",
" ps = [p0]\n",
" for n in range(1, len(a)):\n",
" # この時点でx座標 a[n - 1] まで線が引かれている\n",
" # 前の点から y = f(x) 上の点 (a[n - 1], a[n]) まで垂直に線を引く\n",
" # a[n] = f(a[n - 1]) より、(a[n - 1], a[n]) は y = f(x) 上にある。\n",
" ps.append((a[n - 1], a[n]))\n",
" # 前の点から y = x 上の点 (a[n], a[n]) まで水平に線を引く\n",
" ps.append((a[n], a[n]))\n",
" return ps\n",
"\n",
"def plot_cobweb(f, a):\n",
" \"\"\"クモの巣図法でプロットする\"\"\"\n",
" ps = cobweb(a)\n",
" # y = x をプロットする\n",
" y = x\n",
" plt.plot(x, y)\n",
" # y = f(x) をプロットする\n",
" y = f(x)\n",
" plt.plot(x, y)\n",
" # クモの巣図をプロットする\n",
" plt.plot(*zip(*ps))\n",
"\n",
"b = np.sqrt(2)\n",
"N = 20\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"このように、クモの巣図法を使うと差分方程式の振る舞いを視覚的に把握でき、この場合$a_n$が$2$に収束していることが見て取れる。\n",
"\n",
"他のパラメーターで、クモの巣図を描いてみよう。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.5 [1. 1.5 1.83711731 2.10620335 2.34900532 2.5920257\n",
" 2.8604415 3.18932476 3.64428399 4.38254673 5.91191487]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 1.5\n",
"N = 10\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"テトレーションの底 $b = 1.5$ のときは、明らかに発散している。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.444667861009766 [1. 1.44466786 1.7014207 1.86996122 1.98957349 2.07907521\n",
" 2.14866996 2.20439149 2.25004521 2.28815399 2.32045854]\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = np.power(np.e, (1/np.e))\n",
"N = 10\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"テトレーションの底 $b = e^{1/e}$ のときは $y=f(x)$ と $y=x$ は点 $(e, e)$ で接していて、数列は収束する。\n",
"\n",
"$b \\lt 1$ の場合はどうなるだろうか。"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.5 [1. 0.5 0.70710678 ... 0.64118574 0.64118574 0.64118574]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# x軸は0≦x≦1の範囲で、等間隔に1000点で計算する。\n",
"x = np.linspace(0, 1, 1000)\n",
"\n",
"b = 0.5\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$b \\lt 1$ の場合は、収束値に上下から近づくことになるようだ。"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.1 [1. 0.1 0.79432823 ... 0.39901298 0.39901298 0.39901298]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 0.1\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.06598803584531256 [1. 0.06598804 0.83579319 ... 0.38072659 0.35525403 0.380724 ]\n"
]
},
{
"data": {
"image/png": 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DRWVMuCGD567oQWJCjNvRJEA05BIsJ18A/R+GmWOgaWfoO9rtRBLGvlmfx/2TVrB1bwHX9EnlvkEdqBcX7XYsCTAVejCd9QfYncWPXz/Jd2W7oUkntxNJmCkqLeerHw/yzdLWtE6qx8SRfeiT3tjtWBIkKvRgMgaGvsiz7/zAwq1TYetUtxNJmLr0jCf50wV9iYuOdDuKBJEKPdii61DWpCM9dy7npf3FcN0UaJDidirxsD2HS3hq2mo+X5VDqxbb2Vv3da7pk6IyDwMq9JoQGU1k087Uy/0GPrgRbp4OcQ3cTiUeY61l8tLtjPkki4Licu7u341u7Ztwxyy3k0lN0VEuNSUmHq54G/asgw+ug/JStxOJh+zIL+SmNxfxh/eX0Topgal3nsXv+7cjKkK/4uFEW+g1Kb0fDH2R8smj+OFfN1DU5zbQsb9SDdZa5q07yLtzIij3GR6+qBPXn5FGZIR+rsKRCr2m9biKhTu+5bbcr2Dm79xOIx7RNvVeXrx4OC0T492OIi5SobugsPMw+OorntidR6sz/wfaDXQ7koSQcp+PKct2MnHhVqLr5EDyh4w+v5XKXFTo7nD+O9y+STdO/vIJSO6mUhe/ZO04wAMfL2Pldh/nd+7FVX3hjjkf6rR9AVTo7jrvCcj8Awc+vJ61Fz0DTTq4nUhqqdJyH58vK+Cf8wpoGB/Ny1f35IIuJ7Eib4Xb0aQWUaG7KbYuXP0Rj703gM+XPO12GqnlrC+SC7uP55GLetBI86/IMajQ3Va3CYdTepG24zseOmxh8DOQkOx2KqkFikrLeX/RNr7I2kX9xqspTZjPny7uSL0Ylbkcm1+FbowZBDwPRAJ/s9Y+dYxlLgceASywzFp7VQBzelt0HRIS29J79w/w+aNw0+cQn+h2KnHR1+tyeXDSCrL31eX60/uT0roBLyyZ73YsqeWqLHRjTCQwDhgIZAOLjDGZ1tqsSsu0A/4XONNau88Y0yRYgT0rug5c+R4vZ17L3z/oB1Gx6Bj18GNxxstLi5JoGnU/H95+OqemJfLWqh/cjiYhwJ8t9NOA9dbajQDGmInAMCCr0jK3AuOstfsArLW7Ax00LKSdxY+tTiN+zwqGlcdCx6EQoSlOw8XGvMPMW59LadRGIutsYeqNZxEfo89f/OdPobcAtlV6nA30PmqZ9gDGmPk4wzKPWGs/P/obGWNGAiMBUlN13cJjqteU5KI9jF69mE2Rjcn/r4cgSr/UXravoIT35hUyY+VhOjWrT+/u3/PRxjc0mZYct0DtFI0C2gHnACnAXGNMV2ttfuWFrLXjgfEAGRkZuozPL6nTkPwLnmTY6nHYGTe7nUZqgK8gnXvO/wsjz07nbytXuh1HQpQ/hb4daFnpcUrFc5VlAwuttaXAJmPMWpyCXxSQlGGosPNvsD++zHX7D3Bm09PgzLv+fRFqCX15B4uZMH8zK7bvJ7HFLJqfFMXvzm3rdiwJcf4U+iKgnTGmNU6RjwCOPoJlMnAl8HdjTBLOEMzGAOYMW23bXMCUzV+wYNadznHr2lEa0qy1FJX5KCiKxLd9FA8PPJdFhevZXaDdTlJ9VRa6tbbMGHMHMB1nfHyCtXaVMeZRYLG1NrPitfOMMVlAOXCPtXZPMIOHjfbn88O+JdQv3E/v2GaQ2se5EpKEnP2FpSzYsIeDRbuJqreasVe3ZFDbNBbP1OcpgeHXGLq1dhow7ajnHq503wKjK24SaLH16RHTmN15P7K0eCfE1HU7kRwHi3OSUEFRLJG77uLGsyN4e/MDJNeLczuaeIzOFA0FBmjWix+KdpFcfJiU6IYcbKSjhEJBYYlly64EDpXuIqruOv52Uzt8EQd4e7PbycSLVOihwgDR8aTENOar4l2Qk+t2IvFT1OFLuaHX2byz6XEaJ8SSW+h2IvEqFXooMXCgQXPYvYtuRcWsi6sDkTEaU69lyn2WstK6HN41gDotJnLT2U1p17gh72xyO5l4nQo9RG2qU5diXwm+8iK3o8hRbFk8JiqPZ4cM5Y8/TNQJQlJjdGBzqIqKw6ct81rHlsfRs75zVO+prTXBmtQsFbpIgMQWn0JkZClDujd3O4qEKRW6SDXZ0voADO6crt0Z4ioVukg1tUtKASAyQm0u7lKhi5yg2AjnBK/4aB1bILWDCl3kBMVG6ddHahf9RIqIeIQKXUTEI1ToIiIeoUIXEfEIFbqIiEeo0EVEPEKFLiLiESp0ERGPUKGLiHiECl1ExCNU6CIiHqFCFxHxCBW6iIhHqNBFRDxChS4i4hEqdBERj1Chi4h4hApdRMQjVOgiIh6hQhcR8QgVuoiIR/hV6MaYQcaYNcaY9caY+39lueHGGGuMyQhcRBER8UeVhW6MiQTGARcAnYArjTGdjrFcPeAuYGGgQ4qISNX82UI/DVhvrd1orS0BJgLDjrHcY8DTQFEA84mIiJ/8KfQWwLZKj7Mrnvs3Y0xPoKW1duqvfSNjzEhjzGJjzOLc3NzjDisiIr+s2jtFjTERwFjg7qqWtdaOt9ZmWGszkpOTq/vWIiJSiT+Fvh1oWelxSsVzR9QDugBfGWM2A32ATO0YFRGpWf4U+iKgnTGmtTEmBhgBZB550Vq731qbZK1Ns9amAQuAodbaxUFJLCIix1RloVtry4A7gOnAauADa+0qY8yjxpihwQ4oIiL+ifJnIWvtNGDaUc89/AvLnlP9WOJFK/aBzd/GpJghPHjgYi44JZ0vi651O5aIZ+hMUakxT6b9nXfKBzC8JJMljf/Ic73y3I4k4il+baGLBMK7+2+EtvAMqc4T8//gbiARj9EWuoiIR6jQRUQ8QoUuIuIRKnQREY9QoYuIeIQKXUTEI1ToIiIeoUIXEfEIFbqIiEeo0EVEPEKFLiLiESp0ERGPUKGLiHiECl1ExCNU6CIiHqFCFxHxCBW6iIhHqNBFRDxChS4i4hEqdBERj1Chi4h4hApdRMQjVOgiIh6hQhc5UeUlbicQ+RkVusgJOlBeBMDB/M3uBhGpEOV2AJFQt6nsAABb104FLPjK3Q0kYUtb6CIB8h2FlONj9txHnSf2bXE3kIQdFXqIKvX53I4gv+Dr2EgAXsq8xnli1wooK3YxkYQLvwrdGDPIGLPGGLPeGHP/MV4fbYzJMsYsN8bMNMa0CnxUASgttwAUlR92OYlU5dO6CQBM2voF/5p5n/Nk9mLwWRdTiZdVOYZujIkExgEDgWxgkTEm01qbVWmxJUCGtbbAGDMKeAa4IhiBw5aFkjIfK3Zuhxi3w8jxyI6OJjvauf/Zl/ewt059iDOQvw2a9nI3nHiKPztFTwPWW2s3AhhjJgLDgH8XurV2dqXlFwDXBDJkuCsvt8xat4UCCjExB92OI9XwWqMG/76fP+V21jX6C4caJEBsHRdTiVf4U+gtgG2VHmcDvX9l+ZuBz471gjFmJDASIDU11c+I4e3rdbnsPuDDxCzBuB1GAuq/myYD+VCYT499xfDWMOh8MdhCt6NJiAroYYvGmGuADKDfsV631o4HxgNkZGRoIPFXbMo7BMDn2e8TF1NGqct5JLj2JDTmtqJN8N2f2BYdDdFRsOSf0HEI1GnodjwJEf4U+nagZaXHKRXP/YwxZgDwINDPWqtd+ifIZ2H3wUJueGMZcS3aclLDEurH1QMS3Y4mQZZTFygrIqb4AAMLDnL4k99jpo6G9H6UJDd3O56EAH8KfRHQzhjTGqfIRwBXVV7AGHMK8BowyFq7O+Apw8Ty7HwWbtxHUcxWYtuOwQK5xc5NwsuGGJiRVrEdVbYGdq4BIPK9q52t9g4XQn2VvPxclYVurS0zxtwBTAcigQnW2lXGmEeBxdbaTODPQF3gQ2MMwFZr7dAg5vYUn7Vszz/Exa9+TqOGZ3Bu1/akNU5wO5bUFtbCoV2ctH8nBdlZFEy/F6bfC027kZ96ypGFXI0otYNfY+jW2mnAtKOee7jS/QEBzhU2Fmzcw3ebDlAau4X4do9TDMzeBexyO5nURk/WA+qlVDzaCzkzAYjOvAvaDYH2gyDlNIjUrB7hSJ+6i16ctY5PF6+nRfJQLuvYnzZN6rodSUJNUT51dq+h184N8O04mP88xDaANudCu/OgXoOqv4d4hgrdBcu35wMwK+8l0rs2oGViHdYeNqzd5G4uCV2TmjSCpMFQtB8K9sL+xbDwG/ZHRkBMDHz/JnS5Clr0gohIt+NKkKjQa9DewyU8+skqpqwsIrFVJ9KbxVA3Vh+BBEhEFMQ3dm4AJYdpULiXcwr3k774LVj4d6jTCNLPhfRznFsjzdLhJWqTGpJ3qJgBY+dwsKiUO885ld+eO4LYKG0pSQ0p3AcbZsO6GbBhFqya5DzfqDWk93PKXRfsCHkq9CDbtb+ItTmHOODbQHTK46QmxDL9gGH6FLeTSdhq3RrKU6CsCEoLYfcMyPmCvZERtCAKvvijU/CpfSBGR1uFEhV6kFhrmbhoG09MXU1Znd50adeMtk3qYnQCv9Q21geFe+FgDqcf3A8LXoFvXnCGcJqfAqmnQ6szIbW3M2QjtZYKPQi27Stg1Cc/8u3GPfRJT+SpS35LWpK2dCRElByGrd/C5vmw5ZufCh4DTbtAqzN+utVt4nZaqUSFHkC24tyOyydMIooE7rqgNYM6N6I4Ips1e93NJnJcEltC4gjoOcIZmsnJgl3LYMdSWPkuLJ3gLNcgFZp1Y090xWX3fD6I1HVz3KJCD5A1uw7yxtfZEAdRKa8BMGGzcxPxlKaVh11K4eD3AMT6fPBMa+fQyJRTK24ZEK95iGqKCr2aSsp8vPzVesbNXk/duK5c228MPVvV11i5hBELB3fR7MBuIpK3QfYi+PpZZ2weoHHbn8q9RS9o0gmiYt2N7FEq9GpYui2f+z5azpqcgwzr0Zz/G9KZxARdTkiE4kOwY4lT7tmLYf2XsOw957WIaGjaCZr1gOY9nD+bdlbJB4AK/QSUllv+9GkWE+Zvokm9ON64PoP+HZu6HUuk9oitC637OjdwdjDlb3FKfsdS2LkUsqbAD/9wXo+IhiYdfyr45j2gSWeIjnMlfqhSoZ+Al+Z+x97dBzm/50lcd0YzEmJyWJ6b43YskdqvSRvn1mP4v2eRJHct7Fnn/Ll+KqyaWLFwBDRMhcR0DjWsmJCsMN/5OqMhzWNRofvpQFEpj09di7URFCfMJqH1bOYVwLwv3U4m4iGNE4DKh/gWQVEW7HIuYVxn1uPwxTPO4ZNNO1fcujhb9zHxrkSuTVTofvgyK4cHJ68g92Axw09/ikHd4omJ0qFZIjWm9DBR+dvJKCmF3T9CzipY+k8oOVSxgIFGaZDcAZLbQ9LJzv2kdhBX383kNUqF/iv2HCrmkU+y+GTZDjqcVI/x12bQvWVDt2OJCDjHvOdvcco9ZyXsXg15a2HDzJ/PS1OvuVPyyR0gqT0kV5R9QpJ72YNEhX4M1lqmLN3BmE9Wcai4jNED23N7vzbaKhepTSIiILG1c+t40U/Pl5fBvs2QtwZyK255a+CHt6H08E/L1UmExm0gsU3Fn+nOrXEbiAvNeeRV6EfZkV/IQ5NXMuvH3fRo2ZBnLu1G+6b13I4lIv6KjIKkts6tw4U/Pe/zwYHtFUW/1vlzzwbY/DUsn/jz7xGf9FPZJ6ZD4/Sfij+29vaBCr2Cz2d5Z8EWnvrsR8p9lj9e1IkbzkgjMkJ700U8ISICGrZ0bm2PumpmSQHs2+QU/N6NsHcD7NkIG2fDsnd/vmydRGce+YatKv5MhYZpzv0GLV091FKFXuGu95eyZGMEZ7ZtzJMXdyO1sfaYi4SNmPifjpo5Wslh2LupouQ3OOP2+Vth1wpYM+0/55Gve1Klom/1U/k3SHFuQTyBKqwLvazcx+w1uwFYH/kULbrFkhsTxS2zXQ4mIrVbHaBOEjRPAl85+Moqbkfu74b9OyF/Pmz++ZdGE8ETHW+i+xl3BzxW2Bb66p0HuO/j5azYVZf0dudwSnpd4qJ1BSERCSDrg9ICZyu/5DBFxQeYXrCFNRTTPQhvF3aFXlxWzrhZ63n5qw00jI/mpcvPYXDXERideSYiQZZXmMf0D851JiwLgrAq9O+37OO+j5ezfvchLjmlBX+8qBONNJmWiHhEWBR6QUkZf56+hje/2Uyz+nH8/cZTOfdkXWlFRLzF84U+b10e909aTva+Qq7t04p7B51Mvbhot2OJiAScZwt9f2Epj0/N4oPF2bROSuD9kX3ond7Y7VgiIkHjyUKfvmoXf5y8kj2HSxh1Thvu6t9OR7CIiOd5qtBzDxbzSOYqpq7YScdm9Xnj+lPpmhKaczKIiBwvTxS6tZZJP2zn0U+zKCwp557zT2bk2elE6+rjIhJGQr7Qt+cX8sCkFcxZm0vPVGcyrbZNau/kOSIiweJXoRtjBgHPA5HA36y1Tx31eizwFtAL2ANcYa3dHNioP+fzWd5ZuIWnP/sRCzwypBPXnq7JtEQkfFVZ6MaYSGAcMBDIBhYZYzKttVmVFrsZ2GetbWuMGQE8DVwRjMAAG3IPcf/Hy1m0eR992yXxxMVdaZmoybREJLz5s4V+GrDeWrsRwBgzERgGVC70YcAjFfc/Al4yxhhrrQ1gVgA+WLSNh6asJC4qgj9f2o1Le6XotH0REfwr9BbAtkqPs4Hev7SMtbbMGLMfaAzkVV7IGDMSGAmQmpp6QoFbJyfQv0MTxgzrTJN67s07LCJyvKIjohnYaiApdVOC8v1rdKeotXY8MB4gIyPjhLbeT01L5NS0xIDmEhGpCQ1iGzD2nLFB+/7+HNe3HWhZ6XFKxXPHXMYYEwU0wNk5KiIiNcSfQl8EtDPGtDbGxAAjgMyjlskErq+4fykwKxjj5yIi8suqHHKpGBO/A5iOc9jiBGvtKmPMo8Bia20m8AbwtjFmPbAXp/RFRKQG+TWGbq2dBkw76rmHK90vAi4LbDQRETkeOjdeRMQjVOgiIh6hQhcR8QgVuoiIRxi3ji40xuQCW07wy5M46izUMKB1Dg9a5/BQnXVuZa1NPtYLrhV6dRhjFltrM9zOUZO0zuFB6xwegrXOGnIREfEIFbqIiEeEaqGPdzuAC7TO4UHrHB6Css4hOYYuIiL/KVS30EVE5CgqdBERj6jVhW6MGWSMWWOMWW+Muf8Yr8caY96veH2hMSbNhZgB5cc6jzbGZBljlhtjZhpjWrmRM5CqWudKyw03xlhjTMgf4ubPOhtjLq/4rFcZY96t6YyB5sfPdqoxZrYxZknFz/dgN3IGijFmgjFmtzFm5S+8bowxL1T8fSw3xvSs9ptaa2vlDWeq3g1AOhADLAM6HbXMb4FXK+6PAN53O3cNrPO5QHzF/VHhsM4Vy9UD5gILgAy3c9fA59wOWAI0qnjcxO3cNbDO44FRFfc7AZvdzl3NdT4b6Ams/IXXBwOfAQboAyys7nvW5i30f1+c2lpbAhy5OHVlw4B/VNz/COhvQvuK0VWus7V2trW2oOLhApwrSIUyfz5ngMeAp4GimgwXJP6s863AOGvtPgBr7e4azhho/qyzBepX3G8A7KjBfAFnrZ2Lc32IXzIMeMs6FgANjTHNqvOetbnQj3Vx6ha/tIy1tgw4cnHqUOXPOld2M86/8KGsynWu+K9oS2vt1JoMFkT+fM7tgfbGmPnGmAXGmEE1li44/FnnR4BrjDHZONdf+H3NRHPN8f6+V6lGLxItgWOMuQbIAPq5nSWYjDERwFjgBpej1LQonGGXc3D+FzbXGNPVWpvvZqgguxJ401r7F2PM6ThXQetirfW5HSxU1OYt9HC8OLU/64wxZgDwIDDUWltcQ9mCpap1rgd0Ab4yxmzGGWvMDPEdo/58ztlAprW21Fq7CViLU/Chyp91vhn4AMBa+y0QhzOJlVf59ft+PGpzoYfjxamrXGdjzCnAazhlHurjqlDFOltr91trk6y1adbaNJz9BkOttYvdiRsQ/vxsT8bZOscYk4QzBLOxBjMGmj/rvBXoD2CM6YhT6Lk1mrJmZQLXVRzt0gfYb63dWa3v6Pae4Cr2Eg/G2TLZADxY8dyjOL/Q4HzgHwLrge+AdLcz18A6fwnkAEsrbpluZw72Oh+17FeE+FEufn7OBmeoKQtYAYxwO3MNrHMnYD7OETBLgfPczlzN9X0P2AmU4vyP62bgduD2Sp/xuIq/jxWB+LnWqf8iIh5Rm4dcRETkOKjQRUQ8QoUuIuIRKnQREY9QoYuIeIQKXUTEI1ToIiIe8f+J8h0oHjPV7AAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = np.power(np.e, -np.e)\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"しかし $b \\lt e^{-e}$ になると、もはや値は収束せず、振動するようになる。"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05 [1. 0.05 0.86089166 ... 0.66266084 0.1373594 0.66266084]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 0.05\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.03 [1. 0.03 0.90014741 ... 0.82132737 0.05613297 0.82132737]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 0.03\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"数列 $(a_n)$ の奇数項と偶数項がそれぞれどのように収束するかを、$f(f(x))$ に関するクモの巣図を描いて確かめてみる。"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.1 [1. 0.1 0.79432823 ... 0.39901298 0.39901298 0.39901298]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def plot_cobweb2(f, a):\n",
" \"\"\"数列の偶数項と奇数項をそれぞれクモの巣図法でプロットする\"\"\"\n",
" a_even = a[0::2]\n",
" a_odd = a[1::2]\n",
" ps1 = cobweb(a_even)\n",
" ps2 = cobweb(a_odd)\n",
" # y = x をプロットする\n",
" y = x\n",
" plt.plot(x, y)\n",
" # y = f(f(x)) をプロットする\n",
" y = f(f(x))\n",
" plt.plot(x, y)\n",
" # クモの巣図をプロットする\n",
" plt.plot(*zip(*ps1))\n",
" plt.plot(*zip(*ps2))\n",
"\n",
"b = 0.1\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb2(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05 [1. 0.05 0.86089166 ... 0.66266084 0.1373594 0.66266084]\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 0.05\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb2(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.03 [1. 0.03 0.90014741 ... 0.82132737 0.05613297 0.82132737]\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"b = 0.03\n",
"N = 5000\n",
"a = calculate_a(f, a0)\n",
"plot_cobweb2(f, a)\n",
"print(b, a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"このように、$y=f(f(x))$と$y=x$の交点の数によって $(a_n)$ が収束するかどうかが変わってくることが分かる。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 参考\n",
"\n",
"- [√2の肩に無限に√2を乗せたらなぜ2になるのか - YouTube](https://www.youtube.com/watch?v=LABUpfm-rF0)\n",
"- [テトレーション - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%86%E3%83%88%E3%83%AC%E3%83%BC%E3%82%B7%E3%83%A7%E3%83%B3)\n",
"- [クモの巣図法 - Wikipedia](https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%A2%E3%81%AE%E5%B7%A3%E5%9B%B3%E6%B3%95)"
]
}
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