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@alexalemi
Created September 13, 2014 15:53
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looking at Mellnik's cutting problem
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"cells": [
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"cell_type": "code",
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"input": [
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
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"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try to answer Mellnik's question\n",
"\n",
" > So I was chopping basil yesterday and I started wondering --\n",
"\n",
" > Suppose I have a square, and I make n random cuts across it. Each cut is made by randomly picking a point on the square and randomly choosing an area -- what's the expected distribution of the areas of the resulting polygons as a function of n? \n",
"\n",
" > Not too tricky to do this numerically and maybe there's a good analytical answer. I feel certain that someone has already done this, but I haven't figured out how to talk to the google about it. \n",
" \n",
"Now, I don't know what he means by random area, so I will instead try to answer a different question.\n",
"\n",
"If we randomly choose a point inside a square, and a random direction to make a cut, can we study the distribution of areas formed.\n",
"\n",
"This question reminds me of support vector machines, as we can classify each cut as a single row of the support vector machine, a simple classifier on the plane that satisfies\n",
"\n",
"$$ \\text{sign} ( \\vec w\\cdot ( \\vec x - \\vec b) ) $$ \n",
"\n",
"This separates the plane into two regions, a positive and a negative region. The effect of many cuts will be to choose many of these classifiers, with $w$ a randomly chosen unit vector and $b$ a random point inside the square. The square itself is defined some a simple set of classifiers defining its boundary. \n",
"\n",
"In particular, if I start with some classifiers defining the square, namely.\n",
"\n",
"$$ \\hat x \\cdot \\vec x \\quad -\\hat x \\cdot (\\vec x - \\hat x) \\quad \\hat y \\cdot x \\quad -\\hat y \\cdot (\\vec x - \\hat y) $$\n",
"\n",
"our square is the region that is classified as $(+,+,+,+)$ in this scheme. I will then add $N$ random classifiers and ask for the areas of all of the regions classified as \n",
"\n",
"$$ (+,+,+,+, \\pm, \\pm, \\pm, \\dots ) $$"
]
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"cell_type": "code",
"collapsed": false,
"input": [
"M = 500\n",
"x,y = np.ogrid[0:1:M*1j, 0:1:M*1j]\n",
"z = np.array(np.meshgrid(x,y))\n",
"\n",
"N = 8\n",
"ws = np.random.randn(N,2)\n",
"bs = np.random.rand(N,2)\n",
"\n",
"slots = np.ceil(N/(8.0))\n",
"import matplotlib.colors\n",
"maxn = int(2**(8*slots))\n",
"colors = np.ones((1,maxn,3))\n",
"colors[:,:,0] = np.random.rand(maxn)\n",
"colors[:,:,1] = 0.7\n",
"colors = matplotlib.colors.hsv_to_rgb(colors)[0]\n",
"cmap = matplotlib.colors.LinearSegmentedColormap.from_list(\"randcols\", colors)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 216
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def cut(N):\n",
" ws = np.random.randn(N,2)\n",
" bs = np.random.rand(N,2)\n",
"\n",
" slots = np.ceil(N/(8.0))\n",
" import matplotlib.colors\n",
" maxn = int(2**(8*slots))\n",
" colors = np.ones((1,maxn,3))\n",
" colors[:,:,0] = np.random.rand(maxn)\n",
" colors[:,:,1] = 0.7\n",
" colors = matplotlib.colors.hsv_to_rgb(colors)[0]\n",
" cmap = matplotlib.colors.LinearSegmentedColormap.from_list(\"randcols\", colors)\n",
" \n",
" labels = np.einsum('mj,mjab->mab', ws, z[None,:,:,:] - bs[:,:,None,None]) > 0\n",
" \n",
" q= np.einsum('m,mab->ab',2**(8*np.arange(slots)).astype('int'),np.packbits(labels.astype('int'),0))\n",
" \n",
" sizes = np.array(sorted( filter(None, np.bincount(q.ravel(),minlength=maxn)) ))/(M*M+0.)\n",
" \n",
" return sizes, q, cmap"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 231
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 4"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 240
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig,axs= plt.subplots(4,4, figsize=(8,8))\n",
"for ax in axs.flat:\n",
" sizes,q,cmap = cut(N)\n",
" ax.axis('off');\n",
" ax.imshow(q,vmin=0,vmax=maxn, cmap=cmap, interpolation='none');\n",
"plt.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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"text": [
"<matplotlib.figure.Figure at 0x7fa62cd33f10>"
]
}
],
"prompt_number": 241
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"allsizes = []\n",
"for i in xrange(100):\n",
" sizes,q,cmap = cut(N)\n",
" allsizes.extend(sizes)\n",
" \n",
"plt.hist(allsizes,np.logspace(np.log10(min(allsizes)),0,100), histtype='stepfilled', log=True, normed=True);\n",
"plt.xscale('log');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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W0/b7XjOyhrnwgu5871QqZftZR9U3Yq3yVhm7OCRmfey+PesFJ711ruP0PVgn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\nKR3hTa90eU0AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7fa6178fab50>"
]
}
],
"prompt_number": 242
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 8"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 232
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig,axs= plt.subplots(4,4, figsize=(8,8))\n",
"for ax in axs.flat:\n",
" sizes,q,cmap = cut(N)\n",
" ax.axis('off');\n",
" ax.imshow(q,vmin=0,vmax=maxn, cmap=cmap, interpolation='none');\n",
"plt.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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vlNzxc3J/fpKSR9BKIEH0q3DQfex9QyzjUO69cYM4Q8Yd9XXc4uRDAP7Y5DG4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\n8Hl/PXed7M8hUfjd0g832weLygNSBwxG8lSFol5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4P6O7ZRPJIrNq1GblWZ22+xj5xoel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\nHHmAg95ytaoaFdwdD/80aQ9729NDqawQFcmoGJkczuZqtGbbvyfASdF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"text": [
"<matplotlib.figure.Figure at 0x7fa62d9be990>"
]
}
],
"prompt_number": 233
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"allsizes = []\n",
"for i in xrange(100):\n",
" sizes,q,cmap = cut(N)\n",
" allsizes.extend(sizes)\n",
" \n",
"plt.hist(allsizes,np.logspace(np.log10(min(allsizes)),0,100), histtype='stepfilled', log=True, normed=True);\n",
"plt.xscale('log');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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d1atXZ8hJCAK5Wn1knGdwNVTU0NCQPtac2HLtbOKXfHd3t6nzmpU8iPOaUNjc\nUV7BHer+05f3xPnoo4846KCD2LlzJ9MjEQ4rLWVUwrw8B63+FpL8ypUraWpqSqcF1XlNm0yuAj7X\nHW92k0m2zmtW3pBGeTs57VomebM0M+c1u/gr4rwmFAtlyQQLb7iBWxcuZNuOHZw4bDgAFakU1197\nLTffcAOf79hBfX09p5xyCgDf/OY3mTZtWjoPO29mu/qoPzfKVldX29Z3jUzOa8Y8rOSt4hFZTXpb\nxT6ysrejo4P6+nrq6+vT6UF1XlsHbEMZHnpdTZsGPO/zfWzp7Ox0NCNvJ2d2zUmaXewjzZtREIqV\nW2IVdJSqe1TXjGKfsDK/cF15BZepcxLvRUt5c8UKPlnxHsvjcZ7/85/5Wn09AHPnzmX06NGm9dJY\n1+zOzY6dvhfsyOe7JZN9fpFtoxCi/9BQEngAuBilUZgMTAfmuclUYh/J8JFQmJSHQpSXDHytREMh\natUJ6Nkl5WjTzatLy3hx5fvsXvk+b+/poX3DBq5saJDYRyb5Bz320SHATSi9gCuBmcBl6rWFKM5r\nb6r5n4NLHwWJfSTDR8LQYEo0ypSospnQ/d076B4+3Hb+TWIfBTf2UQtwlsW1HuAij/kKgjCE2bx1\nK3//+9/TL06JuzT4BDJKqgwfyfCRMPQ4MBLhD0uW8N6SJXT29nLECSdw2ZVXAnDIIYcAMnwU5OGj\nnBKE1UdaIcskbyyMI0eOtF19ZBb7SIaPBAFmxcqZpR6/u6eHu5e/zV0XX0x7PM4RX5/DXf9zv6f6\nq/33Y/WRsb7ncvWR1hBZrT7SmDNnTiCGjwJNPuOTSOwjQcieI0rLeFQ9frq3j7f6egfUHbtzs2M/\n6l4+3y2Z7POLotyOUxCE4iEaCrH4pZc4dMIEDp0wgZ+q8ZeE3FCUPQVBEIqHU2PlHBSJktq5i9d7\neninuTnfKhU1gWwUsp1ozqe8hLkQBH+JhkJMVZetftKXYNnu3QPqS6G8H3Ih39TURFNTk0w0a/i1\nrtgv+crKStOJZjtkolkQnNO6cSMPPfggqVSKgw4+mK9//ev09PSwa9euAZtcBe39kAt5LdyFXxPN\nRTmnYDXz70bOKhZJprTu7m7b/JzqJgjCQI4uLeVbX2yj5557WXXnnVx44YVMP/BApk6YwDdOOikt\np69nfta9fL5bzGxyo5NTirJRcBpfyE7O7JqTNLvYR250EwRhIKNLSmgYPoIfDB/BvdWj+KxuP94d\nWc1Dw4YnHCkqAAAXLElEQVTT3dWVltPXMz/rXj7fLWY2udHJKUXZKAiCIAjekEZBEARBSBPIiWZB\nEAS3fNLWxvfOPx+A/SdO5Mc/+UmeNSpMpFEQBKHg+Uo0yv/p6yPx/GLaEwlu29PDqy++CMDEgw/m\nod/+Ns8aFg6BbBSy9VOIx+OOAuLFVR8Cs/y1GCeZ5I2xUMLhsKmfQiQSSX/OuNxU/BQEITvKw2Hm\nDRsGQCKV4vg9e+hr/YS2RIKfrV7N/gsX0tvby/jx4zn55JM9+wUY67uVvFbfzfLXv0fs5Kuqqizf\nP3r5lpYWCYinJ1frhPXxUtzEMamtrbX1UzDLS/wUBME/SkIhZpSVAbArmWR1HD69+x52JpM8WhLm\n0ksvtfys2/qeSz8FpzGb5s6dy9y5cyUgniAIQiYqwmF+XKH0INoTCZ77YivfVLf+HD9pEr966KE8\nahdMBnP1UQnw38AC4A6gbhDvLQjCEGefcJiHR1TxLx+0MGflBzz+xBP5VimQeG0UjgQ+RnnB64kB\nj6JsxbkcOFl37XSgC1gEPAdc7/HegiAIrgmFQnwtFuOfY+WcGIvlW53A4mX46DTgXJQXvHGWc6Ga\ndgwwGWgGpqLs0TwJaFPl2oADPdxbEARByCFeegorgHOA7SZ5XQJog3RrVdnz1fOP2TtktC/wkYd7\nO0JiHwmCkAsk9pE5GyzSJwKjgNW6tFXAUerxs8BIlCGnbwG3eri3IyT2kSAIdpQAO3bv5rjDDuO4\nww7j29/4hqPPDYXYR36uPhqr/u/SpXUB09TjJPBv6vEiH+8rCILgiuHhMH8eNZpdn7WRIMW577/P\nUVOmAFBdW8tLr73Wb2n5UCIXS1KN8wyuF9I3NDSkjzUnNjfOJp2dnY6c1zo7Oy2d17zK9/b2mjqv\nxeNxS3vFeU0QBp+vlJamj1+uHcPOL5RhmG999BHr1q3r5yDm1tnNqr5r8sb6nkke+r9/4vF4enMd\n7V0XROe1Ler/KuBz3fFmtxll67zW2tpq6fChl29tbc24AY5b+Wg0auq8ZiwEesR5TRDyy0Hqzm6g\n1KkJEyZYeiXrsXJGs6rv1dXVdHZ2DqjvdvJm75/W1tb05jpaehCd19YB24ApwOtq2jTgebcZZRvm\nQnoKgiB4JpXqF5oGgtlT0Ghubg5MmIsQ/YeGksADwMUojcJkYDowz23G2fYUrBoEo7ydnBbjJJO8\nMRbKyJEjTXsK2goBs9hH0lMQhABh01Mw1nernoLViiCr0BVm8lpDZPb+0cvPmTOHefPm5XU7zkOA\np1B6AVcC9+uuLURpKN4EHkdZurqFQcZtbBGn15ykVVZW2ubnJk6KIAjBIp/vFv251bEfeOkptABn\nWVzrAS7yro4gCIKQTwIZEC/bOYV8ynd3d5vOKVjJg8wpCEKgSKV49913KSkpIRqNMnz48EC/f7RV\nSEGYU8gZQQid7VW+srLSNnS2GTKnIAjBYVJFBaeokVS37d7NrbfeSkVFBbFYjIsvvrhf/Q7C+0db\nhRTE1UeCIAgFz19H7n0J3xvbxapf3kooBE9u386pp55KXV1xB3guSpc9iX0kCIIfXFVewc/LK/hZ\nrIKRZWXcdttt/OIXv+D2229nz549lp8barGPAo/EPhIEwW9+EC2l75FHab/1Nn72n//JP/7xD0tZ\niX3kM+K8JhPNghA0zld3cAN4QZ3KE+e1QULCXMhEsyAUAvkMc6ExY8aMvDuvCYIgCEWKNAqCIAhC\nmkAOH2WLMT6JFzmza07SKioqbPMzi30kCELh0dzczGeffUY0GmXmzJn9ho1z8W7Rn1sd+0FRNgoS\n+0gQhFxyYiTK/f+q7Bn23vYu3nz7bQ499ND09aEW+0gQBGFIc3NZLH08p7KSRCKRR238ReYUBEEQ\nhDSB7ClIQDzxUxCEQiGZTLJx40ZGjhyZTpOAeD4jAfHET0EQCoVwOMyoUaPYZ599CIfDlJWVWcoW\nQkC8fAwffQdYAxyQqxtI7CNBEAaL0ckUJx5/PDUjRlBRXs7KlSsl9pFLPgDacnkDiX0kCMJg8ZuK\nYXw8Zh8+HrMPR9aMoru7u6BjH7ltFI4EPgYWGNJjwKMo23AuB062yeNDl/cUBEEQBgk3cwqnAecC\nXYBxdnOhmnYMMBloBqai7M98HjADeA5ozE5dQRAEIZe46SmsAM4BtpvkcQnwkHq+VpU9Xz3/HXA1\nAxsEmSEVBEEIGG4ahQ0W6ROBUcBqXdoq4CgL+TOAcSgTzuLeKwiCECD8WJI6Vv3fpUvrAqZZyP9R\n/csZEvtIEIR8IrGPFIzzDJ6HhxoaGtLHmhObW+cOMI8JYpTXjo35a8eZ5M3uYeW8ZqWTOK8JQnGQ\nTCZpa2tj2jTz38Ta+8T4zjJ7sVdXV9u+fzSnNY0gOa9tUf9XAZ/rjjd7zVCc18R5TRAKkXA4TF1d\nnaNNvpxgJ685rWn45bzmR6OwDtgGTAFeV9OmAc97zVDCXEhPQRAKkWQyyfvvv8+IESOoqamhrq6u\n3w+3Yg1zEaL/0FASeAC4GKVRmAxMB+Z5VUp6CtJTEIRC5KBwiJ9ddx0An+/ezct//SsnnHBC+noh\nhLlw0ygcAtyE0gu4EpgJXKZeWwjch+K8FkFZurplYBaCIAjFy3+VlUNZOQDnxcqJx+N51sg9bpak\ntgBnAWOAr7K3QQDoAS5CcV47mjw7qUnsI0EQgkrQYx8FMkpqtnMK2nkmef0qAGP+nZ2dA2b/zeQ1\nOY2uri7TOYV4PJ6WNyJzCoIwNOjo6OCTTz4Z8B7Q3g96jPHS9O8fvfySJUtYs2ZNoFYf+U62cwqt\nra2OZv9bW1szjve7lY9Go6ZzCsaXvh6ZUxCEoYH2w9BY363eD1bvH738jBkzmDdvXqBWHwmCIAgm\nPPrIIyxtaiIUCnHlVVcxbty4fKuUEWkUBEEQcsB3kyneX/wCvcCziQRHHnUUZ5xxRr7Vyog0CoIg\nCDngxFiME2MxAFp6e/KsjXMC2ShkO9Ecj8fp6OjIKB9XJ4HN8tfczjPJG93Tw+Gw6URzJBJJf844\nXyATzYIwNOjo6Oj3HtHQ3g96qqqqLN8/evmWlhYWLVokE80auXJG02QyyRuv1dbW2jqvmeUlE82C\nMDRw877Sv4PsmDt3LnPnzi3oPZoFQRCEgCKNgiAIgpBGGgVBEAQhjTQKgiAIQpqibBQk9pEgCEEl\n6LGPirJRsNqJzY2c2TUnabt27bLNz6lugiAUJ17fLWY7sFl9NhsCuSTVj4B4TvwUOjs7Lf0UvMr3\n9vZaBsSzQvwUBGFooL1PjPXd6v1g9f7Ryzc3N4ufgh4JiCd+CoJQKBRCQLyiHD4SBEEIEqV9Cb47\nfz771ozi2COPpKmpKd8qWTLYPYU5wBHARqAeuBb4YpB1EARBGFRuj5XTUVoKwI17eti4cWOeNbLG\nbU/hSOBjYIEhPQY8irId53LgZIvPfwDcAiwCPkfZqc13jPGIvMiZXXOSVlFRYZufU90EQSgeykMh\n6koi1JVEqAiXDLju5N2iP7c69gM3PYXTgHOBLsA4u7lQTTsGmAw0A1NR9mk+D5gBPMfebTrrgGHA\nCx71tsVtbBGn15ykVVZW2ubnJk6TIAhFiMk8oJN3i/7c6tgP3PQUVgDnANtN8rgEeEg9X6vKnq+e\n/w64mr0NwlHAvwDXAPu5V1kQBEHIFW4ahQ0W6ROBUcBqXdoqlJe/kTkoQ0dTgXuB4O84IQiCMITw\nY6J5rPq/S5fWBUwzkV2i/gmCIAgBxM/VR8Z5Bs8L6BsaGtLHmhObG+c1cOfs5qd8d3e3qfOalTyI\n85ogDCVSqSRbtmzpV+e9vH9WrlzZb2lrkJzXtqj/q1BWFGnHm71mmK3zmpU3s1HeTk67lkneLM3M\nec0u9pE4rwnC0CFEiDFjxvSr81axj6zePx0dHdTX11NfX59O98t5zY9GYR2wDZgCvK6mTQOe95qh\nH2EuwHxW3ug2rh0b8+/s7KS6ujqjvCan0dXVZRnmQpM3Ij0FQRg6JE16Ctr7QY8xXpr+/aOXX7Jk\nCWvWrMlrTyFE/6GhJPAAcDFKozAZmA7M86qUhLmQnoIgFCuh0MCeQpDCXLhpFA4BbkLpBVwJzAQu\nU68tBO5DcV6LoCxd3TIwC0EQBEHjnXfeoampiW3btlFTU8OZZ56Z8YdnrnHTKLQAZ1lc6wEuyl4d\nQRCEocN9d97Jmmf+wJTSUv60p4dwOMwPf/jDvOoUyCipEjpb5hQEoVhJpVLpOYXu7m6+UVrK+cMq\nWRge6DYmobNVgrD6SIsnkkneGHdk5MiRtquPqqqqBswXyJyCIAwdwqFwek6hctgwSznth6fV6iON\nOXPmSOjsTEjsI0EQAovDH3KFEPtIEARBKHKkURAEQRDSBHJOIduJ5nzKS5gLQRDs0Ie56N6501bW\nyfunqamJpqYmmWjWMJtozqd8ZWWl6USzHTLRLAhDh5DDiWZw9v7Rwl3IRLMNZnFE3MpZxSLJlNbd\n3W2bn1PdBEEoUhz27o3vCv251bEfFGWjYNbdcitnds1J2q5du2zzc6qbIAjFSWpAQGlzrGK62R37\nQVE2CoIgCII3pFEQBEEQ0kijIAiCIKSRRkEQBEFIE8glqdn6KcTjcUcB8eKqD4FZ/lpMo0zyxthH\n4XDY1E8hEomkP2dcbip+CoIwdEilcOSnUFVVZfn+0d4nAC0tLRIQT0+u/A70sYrcxEiqra219VMw\ny0v8FARh6BAOO/NTcBovbe7cucydO1f8FARBEAT/GcyewliUTXq+AE4C/gC8OIj3FwRBEDLgpqdw\nJPAxsMCQHgMeRdmKczlwssXnNwP3AjVAFfC2G0UFQRCE3OO0UTgN+BHQBQPc8RaqaccA5wJPAGPU\na+cB9wCzdfK/Ah4DrveksSAIgpAznDYKK4BzgO0mn78EeEg9X6vKnq+e/w64GmgEjkUZQgL4FMjZ\n7tQS+0gQhMBSJLGPNlikTwRGAat1aauAo0xkoyi9iguA7wO/cHhv10jsI0EQgkrQYx9lO9Gs/fLv\n0qV1AdNMZJvUP4Df2GXa0NCQPtb8Fdz4KXR2djryU9BvhO0kfyfyvb29pn4K+o22jYifgiAMHVKp\nlKf9FPTvn3g8nt5HQXvXBc1PwfhmymrxfLZ+Cq2trZZre/Xyra2tGfc6cCsfjUZN/RSML3094qcg\nCEOHUCjkaT8F/funtbU1vY+Clh4UP4Ut6n+9W28VykojQRAEocDItqewDtgGTAFeV9OmAc9nk2m2\nYS5k+EgQhKDi1/CRRnNzc17DXIToPzSUBB4ALkZpFCYD04F52SiV7fCRVYNglLeT02IaZZI3xj4a\nOXKk6fCRtkLALPaRDB8JwtAh7HA7Tu2Hp9n7R7/iaM6cOcybN8+34SOnb5RDgJuArwGfoCw7vUy9\nVgbch9JbiAD/jrIE1RONjY2pWbNmef24L9xzzz1cc801WeVxaVU1jTu7Wd/bayvz0Z4emixWLGky\nRv6ns/8StPNHjKQiLBFLBKEQMNbfYaEQ542sGpDulsbGRmbPnp31r0SnPYUWlBAVZvQAF2WrSJAY\nN24c48aN8/z5Y445hoNmzqR22zYWLVrUbzhJY9q0aRx0yimM7+lh/f3302vSeOy3334cdPbZA9K/\n/MgjbNu2DYDhw4cz/Xvfkx6DIBQI325u5o033kifn3322ey3337Mf/99Xn755TxqphC4N0ljY2Pq\nT3/6U1ZzCiIv8iIv8kNFXluaevzxx/vSUwhko5Dv4SNBEIRC45VXXvGlUZCBaEEQBCFNUTYK+Yx9\nlCk+iR9xSvJln5WtfsdhGSz7vMSWGSz73Npmlp4P+3L17MzSh1LdM54HIfZRQZHP2EeZ4pP4Eack\nX/ZZ2ep3HJbBss9LbJnBss+tbWbp+bAvV8/OLH0o1T3jeZBjH+WEQnZe0++jauVskkl/J/oYnd3c\nTlQ51Ue7l9Efw0ofvXyuJ9rs9DF+R5nk9bqD9fejf75e9XdSPs30d1s+7ew1PjMn9cWJvYP1/Why\nTu1tbW11Xd+96g+Z65fxO3JSHwfLeS1wNDY2prJl/fr1WcuZXXOSpj83O3aqmx35ss/KVjsZLwyW\nfW6fnRvd7HCSh1vbzNLzYV+unp1Z+lCqe8Zzs+PGxkZfwhsU5fCRIAiC4A1pFARBEIQ0JflWwMj8\n+fMXTpw4Met8ysvLs5Yzu+YkTX9uduxUNzvyZZ+VrXYyXhgs+9w+Oze62eEkD7e2maXnw75cPTuz\n9KFU94znxuPW1lYee+yxmx0pZ4M4rwmCIBQB4rwmCIIg+I40CoIgCEKaovRTEHmRF3mRHyry+oB4\nfiBzCoIgCEVAIc8pfBNYn8sbBDk+SSHHX5HYRxL7KBMS+yiznMQ+6k8lcFyubxLk+CSFHH9FYh9J\n7KNMSOyjzHJBj33kplE4EvgYWGBIjwGPAm8Cy4GTbfL4V+AOAjhsNVg0NzfnW4WcIvYVNsVsXzHb\n5idOG4XTgB8BXYAxvsZCNe0Y4FzgCWCMeu084B5gNkqj0gZsyUrjAqfYC6bYV9gUs33FbJufOG0U\nVgDnANtNPn8J8JB6vlaVPV89/x1wNdCIMmyUAC5EGUZaQI48qp0+fDs5s2tO0vTnVsfZki/7rGz1\nu7INln35eHZO83Nrm1l6MZVNs/Risi8o7xZw3ihssEifCIwCVuvSVgFHmcjeBTyCMnSUArpRGgnf\nKfYHJ41CZjlpFIqrbJqlF5N9QXm3gPux/VdRXuyPqefHAv8LlAG9atpPUYaSZntR6De/+c3H48aN\nm+Tls4IgCEOV9vb2dRdccMGB2ebjl/OacZ7B80SyH0YJgiAI3sh2Sao2aazf9qgK2JxlvoIgCEIe\nyLZRWAdsA6bo0qahLE0VBEEQCgy3jUKI/kNDSeAB4GL1fDIwHWXVkSAIglCkHAI8hTJc9BZwv+5a\nGcrks+a85mmCWRAEQRAEQRAEQRjC5DwgoiB45DvAGuCAfCuSTwK5n0IGrkCZ3N4PeBf4a37V8Z1X\n2esMeCdKIS0WBiUgYp4YC5wFfAGcBPwBeDGvGvnLHOAIYCNQD1yLYmsx8QFKKJ5iogS4DXgfZb73\ndjLYONhRUrMNqvfPwAwgijLh/W5OtPSOH0EDN6A4BLZg7UmeD4o9IGK29m0G7gVqUJZlv50TLb2T\nrX0fALcAi4DPURxUg4Qf5fPDnGjmH15sPB0lZt0i4Dng+kw3GcyewmkoAfMyBdWbDDQDU1Emts9D\naQieQ2npUsBvgBNRCunluVfdEX7Y14gSK6oLpQG8BWjIveoZ8cO2DoIbENGvZwfwK+BTlMr3bznW\n2yl+2lcHDANeyLXSLvDTvqDi1cZJ7O0ZtAGBcg7eX/3/KjBflx4GttJ/WKER5VelkXNRYigBHAo8\n7bOO2eCHffuiDEMAHAY847OOXvHDtgbgIpSAiFvJYUBED/hh37HsfXbTUYaPgoIf9oES0+xqlB+T\nQRp398s+LY/xvmrnD15tPBP4sXpcjzIkbctgDh/5EVTvKZQlsBeifDE3+6hftvhh30jgRpQos5cA\nP/FTwSwoqICIHvDDvijKL7YLgO8Dv/BRv2zxw745KEMQU1GGyc7wU8Es8cM+UGwahzLhPHDD5Pzi\n1cZnUd4rC4BvAbdmulEQJpq1X1ddurQuFM9oI70oFa6QcGPfKuAq9fi3uVTKJ9zYpvGI+lcIuLGv\nSf0DZXizEHBj3xL1r5BwWz7/qP4VEplsTLJ3GHORkwzzsUezFb4F1QsoxWxfMdsGYl+hU+z2gY82\nBqFRKPagesVsXzHbBmJfoVPs9kEObAxCo1DsQfWK2b5itg3EvkKn2O2DHNiYj0ah2IPqFbN9xWwb\niH1iX/ApKhuLPaheMdtXzLaB2Cf2BZ+hYKMgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIgCIIg\nCIIgCIIgCIIgCIIgCEXP/wewETN7WTRbxAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fa630701690>"
]
}
],
"prompt_number": 234
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 16"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 236
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"allsizes = []\n",
"for i in xrange(100):\n",
" sizes,q,cmap = cut(N)\n",
" allsizes.extend(sizes)\n",
" \n",
"plt.hist(allsizes,np.logspace(np.log10(min(allsizes)),0,100), histtype='stepfilled', log=True, normed=True);\n",
"plt.xscale('log');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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lUqRSqUFPtZL7yL2sXHIfhRg8NDQA3AdcAjyLsiT1GGCem0ol95EMHwnlz+j+\nAa696iquveoqevbu5d5f/IL58+cP0pHcR870Ifi5j6YAP0B5CrgCOB64TN23CPgZSvBaFGXpqqsY\nBcl9JMNHQvlzTaKGaxJKMOf30t3s3r17iI7kPsqtXy65j9qAsy329QLzLfYJgiAIASaQWVJl+EiG\nj4TKwuoyleEjZ/oQ/OGjohKE1UfaRZZL33gx1tXV2a4+qq+vHzI0JMNHQqUTzWS4YfFifqG27WsW\nL2b8+PGu2q92Y3bbfrVPL1YfGdt7MVcf2fmr158zZ46nw0cV+eY1P/OTSO4jQRjKVdUJ7ifMT1I7\nmbxlKwu//nUmjT2ESWMP4aGHHhqka/cPndNts7IXbc/Pe0su/7wikE8KgiBUFnXhMJ+oqgLgh9Eo\nX+3vh949LNndlX2zmxAMpFMQBKGkJMJhDleHWJsiEZ+tEYwEslModKLZT31JcyEIzkmEQtz0k59w\n1y23AHDlwoVc8tWvlk17D4L+qlWrWLVqlUw0a3i1rtgr/WQyaTrRbIdMNAvDla/VJvmy+mKqB3bv\nZveuXbbtJWjtPQj6WroLmWi2wWrm342eVS6SXLKuri7b+pzaJgjDgXAoREM4QkM4Qk0oxBtvvcWD\nDz7IY489xqZNmwbpGtuO3bZZ2Yu25+e9JZd/XlGRnYLkPhKE8uNTsSr616zhoW9+k+suuoifLF48\naL/kPiqP3EeCIAieMD0eZ7pafnBvP+26uTmhdFTkk4IgCIKQH/KkIAhC4AgBT/zxj2w89lgAzr34\nYmZ/4Qv+GjVMkCcFQRACxxmJGm4lxOXtm5j8+gae8WhljZCbQD4pFBqnkE6nHSXUSqsxBGb1azlO\ncukbc6GEw2HTOIVoNJr9nnG5qcQpCMJgkuEwJ8arAdja389qlLZj1x71bVHfftO6pJSFJsQztncr\nfa29m9Wvt8NO385fvX5bW5skxNNTrHXC+nwpbvKYNDU12cYpmNUlcQqCYE0iFOK3TzzB/4wbB8AF\nF17IrXffbfsdp+3X7Htu2nsx4xSc5mxqbm6mubnZ9/cpCIIglITTqhPMqIqTAVb0pnlm40a/Tapo\nStkpRIAbgVdQXtF5M7C5hL8vCEIZEgqFaFRzJI0IyTRoscn3CE8F3gQuNsirgQdQXsW5BjhFt+8M\noBNYAvwB+E6evy0IwjAlBKz5+9/58txmvjy3mXvvustvkyqOfJ4UTgfOQ7nBG2c5F6my44CJQCsw\nCeUdzRP+3NZjAAAWOklEQVTY92SwGTgsj98WBGEY89l4nO/2psk89zzr9/bxu48/4rIrr/TbrIoi\nnyeFl4FzgZ0mdV0K3K9uv6HqXqBuvwkcqJYPAoo2MCi5jwShMkmGw3wxUcMZNTUcVxUftE9yH3lD\nPp3CexbyQ4FGQP/GjPXANLX8OFCHMuT0ReA/8/htR0juI0EYHry7ZQt33HEHd9xxB0899VRWLrmP\n8sfLiebR6menTtYJTFbLA8C31PISD39XEIRhyORYjBNTnaxbvJitfX1sP/hgzj//fL/NKnuKsfrI\nOM/geiH9woULs2UtiM1NsEkqlXIUvJZKpVwFszjR7+vrMw1eS6fTlv5K8JoguGd0JMLimloAXgz1\ncoNJW9Dab3t7u+v2rsetvlV719vjRh8G33/S6XT25TravS6IwWvb1c964ENdeZvbigoNXmtvb7d9\n+be2r729PecLcNzqx2Ix0+A140WgR4LXBKE4NDQ0kEqlsm3QTXt3Wr+ZvlV719vjVN/s/tPe3p59\nuY4mD2Lw2lvAx8CRwLOqbDLwpNuKCk1zIU8KgiBAZT8paLS2tgYmzUWIwUNDA8B9wCUoncJElCC1\neW4rLvRJwapDMOrb6Wk5TnLpG3Oh1NXVmT4paCsEzHIfyZOCIBTO7p4eVq5cCcCIESMYP378oFQR\ndu1dI9eTgrG9W+lbrQiySl1hpq91RGb3H73+nDlzmDdvnq9PClOAH6A8BVwBHA9cpu5bBPwMJXgt\nirJ0dfvQKoqL29wiTvc5kSWTSdv63DyaCoLgjIMiEZp27uK6c75M194+omPGsHb9esDbtufnvUW/\nbVX2gnw6hTbgbIt9vcD8/M0RBEFwz8HRKI+omUNfJcR3+vp8tqh8CWRCvELnFPzU7+rqMp1TsNIH\nmVMQhGIRtPtDMfS1VUhBmFMoGkFInZ2vfjKZtE2dbYbMKQiCt2z58EP+77//OwCHH3EE8y+5xNH3\ngnY/caKvrUIK4uojQRAE3zksGuWre3rZ+9Of8dHAAL+rG+m4UxAq9HWckvtIEIYviXCYf0uOYMGI\nkVxYW5sdzpXcR86oyE5Bch8JgqCxO53m6aef5oknnuCVV14pqC7JfeQTErwmE82C4AWN4QiTMhl+\nOG8e6b39bI5EeHbtGglesyGQnYKkuZCJZkHwgvpwmAdrRwCwObqXM/bssW3D5ZTmQmPGjBmeBq9V\n5PCRIAiCkB/SKQiCIAhZKrJTMOYnyUfPbJ8TWU1NjW19Tm0TBCF4+Hlv0W9blb2gIjsFyX0kCEIx\nGA65jyqyUxAEQRDyQzoFQRAEIUsgl6RKQjyJUxCEYjAw0G/bHoN2P5GEeCqSEE/iFAShGITDQ9ua\nnqDdT/xIiOfH8NE5wAbgkGL9gOQ+EgShGEjuo+LwKrC5mD8guY8EQSgGwyH3kdtOYSrwJnCxQV4N\nPIDyGs41wCk2dfzD5W8KgiAUTDUhtqdSJKurSVZXc/QRR/htUiBxM6dwOnAe0AkYZzcXqbLjgIlA\nKzAJ5f3M5wMzgD8ALYWZKwiCkB/7RSL844AxDGQydGYGmP3++36bFEjcPCm8DJwL7DSp41LgfnX7\nDVX3AnX7IWABQzsEmSEVBKGkJEIhasNhakKyGt8KN0fmPQv5oUAj8LpOth6YZqH/JWAMyoSzhPcK\nglByIsCunh6OnjCBoydMYLZHyzkrAS+WpI5WPzt1sk5gsoX+Y+pf0Qh67qNcy00FQSguI8JhVo7a\nn55dXfRl4EvvvODoe8Mh95GXcQrGeYa8h4cWLlyYLWtBbG6DO8A8J4hRXysb69fKufTNfsMqeM3K\nJgleE4TSc2g0BsAeXRvKFSxmbL92+mZo+sbvmOk3NDTY3n+0oDWNIAWvbVc/64EPdeVt+VYowWsS\nvCYIfhC0+4mdvha0puFV8JoXncJbwMfAkcCzqmwy8GS+FUqaC3lSEAQ/CNr9pFzSXIQYPDQ0ANwH\nXILSKUwEjgHm5WuUPCnIk4Ig+EHQ7idBT3MxBViG8hRwBXCvbt8ilI7iBeBhlKWr2xEEQRDKCjed\nQhtwNrA/MB24TLevF5iPErx2LD4HqUnuI0EQisFwyH0UyCyphc4paNu59PWrAIz1p1KpIbP/Zvqa\nnkZnZ6fpnEI6nc7qG5E5BUEIBrnG8I3t3Upfa+9m9W/atGnId8z0jfnS9Pcfvf7y5cvZsGFDoFYf\neU6hcwrt7e2W43B6/fb29pzj/W71Y7GY6ZyC8aavR+YUBCEYeDXmb9XetY7F2N7t9M3uP3r9GTNm\nMG/evLJOnS0IgiAEFOkUBEEQhCzSKQiCIAhZAjmnUOhEczqdpqOjI6d+Wp0ENqtfCzvPpW8MTw+H\nw6YTzdFoNPs943yBTDQLQjDINdFsbO9W+lp7N6tffx+x06+vr7e8/+j129raWLJkiUw0axQreETT\nyaVv3NfU1GQbvGZWl0w0C0IwcNveixm8pr8H2dHc3Exzc7NMNAuCIAjeE8gnBUEQhFKSyWR47z3l\nlTE1NTU0Njb6bJF/SKcgCMKwJgJMqKlhxmTlFTAfptN0p9NEIhF/DfMJ6RQEQRjWREIhVozcN4E8\nrnvzsF7AUZFzCpL7SBCEYjAcch9VZKdg9SY2N3pm+5zIuru7betzapsgCMHDz3uL2RvY3NjklEAO\nH3mREM9JnEIqlbKMU8hXv6+vzzIhnhUSpyAIASKTobW1lUgkQjwez8YnuHkJjlV71/SN7T2XPgy+\n/+j1W1tbJU5BjyTEkzgFQfCSSbVJzjn1VAB29PSQ6uyktrbWVLcSE+IFslMQBEHwi+Uj67LlSXv2\n8I3LLiMej1NdU8NlV17po2WlodSdwhzg08AHwEzgauCjEtsgCILgiJtrk+x48o8A/GdPN+ecf77P\nFhUftxPNU4E3gYsN8mrgAZTXca4BTrH4/qvADcAS4EOUN7V5jjE/ST56ZvucyGpqamzrc2qbIAj+\n84VEDV+pTfKV2iS1sRgjR4509L1i3Fv021ZlL3DzpHA6cB7QCRhnNxepsuOAiUArMAnlPc3nAzOA\nP7DvNZ0HArXAU3nabYvb3CJO9zmRJZNJ2/rc5EkRBCFYOL0BF+Peot+2KnuBmyeFl4FzgZ0mdVwK\n3K9uv6HqXqBuPwQsYF+HMA04C/gGcLB7kwVBEIRi4aZTeM9CfijQCLyuk61HufkbmYMydDQJuAv4\nkovfFwRBEIqMFxPNo9XPTp2sE5hsortc/RMEQRACiJerj4zzDHkvoF+4cGG2rAWxuQ0e8Uu/q6vL\nNHjNSh8keE0QyhU/7z/r1q1j1apVWVmQgte2q5/1KCuKtPK2fCssNHjNKprZqG+np+3LpW8mMwte\ns8t9JMFrglAepFIpDjzwwOy2VfCaVT4iqwUnVrmPrO4/HR0dzJw5k5kzZ2blQQpeewv4GDgSeFaV\nTQaezLdCL9JcgPmsvDFsXCsb60+lUjQ0NOTU1/Q0Ojs7LdNcaPpG5ElBEMqDnTsHr7OxS3Nhdf/Z\ntGmT6SuEjfrGfGn6+49ef/ny5WzYsMHXJ4UQg4eGBoD7gEtQOoWJwDHAvHyNkjQX8qQgCOVAJaa5\ncLP6aAqwDOUp4ArgXt2+RSg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"text": [
"<matplotlib.figure.Figure at 0x7fa62e3b0450>"
]
}
],
"prompt_number": 238
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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