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Peter Norvig authored and 
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@@ -104,8 +104,9 @@
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"source": [
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"def do(n, h=1, colors='RB') -> dict: \n",
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" \"\"\"A dict of {(w, h): mean-cluster-size} for grids with width w from 1 to n, and with height h.\"\"\"\n",
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" return {(w, h): mean(map(mean_cluster_size, grids(w, h, colors)))\n",
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" for w in range(1, n + 1)}"
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" for w in range(1, n + 1):\n",
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" μ = mean(map(mean_cluster_size, grids(w, h, colors)))\n",
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" print(f'{w:2} × {h} grids: {μ:6.4f} mean cluster size')"
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]
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},
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{
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@@ -121,44 +122,32 @@
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "ee733740-c0b2-490b-9541-1b07e37a6056",
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"id": "e004289f-0c81-46ab-8900-9312a0aa6f7c",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 1.29 s, sys: 43 ms, total: 1.33 s\n",
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"Wall time: 1.34 s\n"
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" 1 × 1 grids: 1.0000 mean cluster size\n",
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" 2 × 1 grids: 1.5000 mean cluster size\n",
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" 3 × 1 grids: 1.7500 mean cluster size\n",
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" 4 × 1 grids: 1.8750 mean cluster size\n",
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" 5 × 1 grids: 1.9375 mean cluster size\n",
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" 6 × 1 grids: 1.9688 mean cluster size\n",
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" 7 × 1 grids: 1.9844 mean cluster size\n",
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" 8 × 1 grids: 1.9922 mean cluster size\n",
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" 9 × 1 grids: 1.9961 mean cluster size\n",
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"10 × 1 grids: 1.9980 mean cluster size\n",
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"11 × 1 grids: 1.9990 mean cluster size\n",
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"12 × 1 grids: 1.9995 mean cluster size\n",
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"13 × 1 grids: 1.9998 mean cluster size\n",
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"14 × 1 grids: 1.9999 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 1): 1.0,\n",
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" (2, 1): 1.5,\n",
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" (3, 1): 1.75,\n",
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" (4, 1): 1.875,\n",
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" (5, 1): 1.9375,\n",
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" (6, 1): 1.96875,\n",
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" (7, 1): 1.984375,\n",
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" (8, 1): 1.9921875,\n",
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" (9, 1): 1.99609375,\n",
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" (10, 1): 1.998046875,\n",
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" (11, 1): 1.9990234375,\n",
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" (12, 1): 1.99951171875,\n",
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" (13, 1): 1.999755859375,\n",
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" (14, 1): 1.9998779296875,\n",
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" (15, 1): 1.99993896484375}"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(15)"
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"do(14)"
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]
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},
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{
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@@ -187,31 +176,20 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 8.12 s, sys: 269 ms, total: 8.39 s\n",
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"Wall time: 8.71 s\n"
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" 1 × 2 grids: 1.5000 mean cluster size\n",
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" 2 × 2 grids: 2.1250 mean cluster size\n",
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" 3 × 2 grids: 2.4688 mean cluster size\n",
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" 4 × 2 grids: 2.6682 mean cluster size\n",
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" 5 × 2 grids: 2.7920 mean cluster size\n",
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" 6 × 2 grids: 2.8737 mean cluster size\n",
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" 7 × 2 grids: 2.9305 mean cluster size\n",
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" 8 × 2 grids: 2.9717 mean cluster size\n",
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" 9 × 2 grids: 3.0027 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 2): 1.5,\n",
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" (2, 2): 2.125,\n",
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" (3, 2): 2.46875,\n",
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" (4, 2): 2.6682291666666664,\n",
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" (5, 2): 2.7920386904761907,\n",
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" (6, 2): 2.873721168154762,\n",
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" (7, 2): 2.9304973563762626,\n",
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" (8, 2): 2.971709969311288,\n",
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" (9, 2): 3.0027141140414764}"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(9, 2)"
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"do(9, 2)"
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]
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},
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{
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@@ -238,28 +216,17 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 6.52 s, sys: 170 ms, total: 6.69 s\n",
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"Wall time: 6.72 s\n"
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" 1 × 3 grids: 1.7500 mean cluster size\n",
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" 2 × 3 grids: 2.4688 mean cluster size\n",
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" 3 × 3 grids: 2.8986 mean cluster size\n",
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" 4 × 3 grids: 3.1591 mean cluster size\n",
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" 5 × 3 grids: 3.3266 mean cluster size\n",
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" 6 × 3 grids: 3.4408 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 3): 1.75,\n",
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" (2, 3): 2.46875,\n",
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" (3, 3): 2.8986049107142855,\n",
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" (4, 3): 3.1591145833333334,\n",
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" (5, 3): 3.326567058836346,\n",
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" (6, 3): 3.4407984463961334}"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(6, 3)"
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"do(6, 3)"
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]
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},
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{
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@@ -272,27 +239,16 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 27.9 s, sys: 952 ms, total: 28.9 s\n",
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"Wall time: 29.1 s\n"
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" 1 × 4 grids: 1.8750 mean cluster size\n",
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" 2 × 4 grids: 2.6682 mean cluster size\n",
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" 3 × 4 grids: 3.1591 mean cluster size\n",
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" 4 × 4 grids: 3.4616 mean cluster size\n",
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" 5 × 4 grids: 3.6608 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 4): 1.875,\n",
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" (2, 4): 2.6682291666666664,\n",
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" (3, 4): 3.1591145833333334,\n",
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" (4, 4): 3.461628834083668,\n",
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" (5, 4): 3.6608226758600444}"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(5, 4)"
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"do(5, 4)"
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]
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},
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{
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@@ -315,34 +271,21 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 13.1 s, sys: 510 ms, total: 13.6 s\n",
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"Wall time: 13.7 s\n"
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" 1 × 1 grids: 1.0000 mean cluster size\n",
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" 2 × 1 grids: 1.3333 mean cluster size\n",
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" 3 × 1 grids: 1.4444 mean cluster size\n",
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" 4 × 1 grids: 1.4815 mean cluster size\n",
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" 5 × 1 grids: 1.4938 mean cluster size\n",
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" 6 × 1 grids: 1.4979 mean cluster size\n",
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" 7 × 1 grids: 1.4993 mean cluster size\n",
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" 8 × 1 grids: 1.4998 mean cluster size\n",
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" 9 × 1 grids: 1.4999 mean cluster size\n",
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"10 × 1 grids: 1.5000 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 1): 1.0,\n",
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" (2, 1): 1.3333333333333333,\n",
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" (3, 1): 1.4444444444444444,\n",
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" (4, 1): 1.4814814814814814,\n",
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" (5, 1): 1.4938271604938271,\n",
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" (6, 1): 1.4979423868312758,\n",
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" (7, 1): 1.4993141289437586,\n",
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" (8, 1): 1.4997713763145861,\n",
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" (9, 1): 1.499923792104862,\n",
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" (10, 1): 1.4999745973682874,\n",
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" (11, 1): 1.4999915324560957,\n",
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" (12, 1): 1.4999971774853653}"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(12, 1, 'RGB')"
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"do(10, 1, 'RGB')"
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]
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},
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{
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@@ -367,28 +310,17 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 10.5 s, sys: 412 ms, total: 11 s\n",
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"Wall time: 11.3 s\n"
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" 1 × 2 grids: 1.3333 mean cluster size\n",
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" 2 × 2 grids: 1.6543 mean cluster size\n",
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" 3 × 2 grids: 1.7737 mean cluster size\n",
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" 4 × 2 grids: 1.8261 mean cluster size\n",
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" 5 × 2 grids: 1.8535 mean cluster size\n",
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" 6 × 2 grids: 1.8698 mean cluster size\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"{(1, 2): 1.3333333333333333,\n",
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" (2, 2): 1.654320987654321,\n",
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" (3, 2): 1.7736625514403292,\n",
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" (4, 2): 1.8261240664532845,\n",
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" (5, 2): 1.8535078615096905,\n",
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" (6, 2): 1.8697928838761029}"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"%time do(6, 2, 'RGB')"
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"do(6, 2, 'RGB')"
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]
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},
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{
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@@ -396,7 +328,7 @@
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"id": "3c18f723-447f-4cd6-ba27-59db37e87659",
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"metadata": {},
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"source": [
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"By the same reasoning as we had last time, this should converge to 3/2 + 3/2 × 1/3 = 2. "
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"By the same reasoning as we had last time, this should converge to 3/2 + 3/2 × 1/3 = 2. (But it would take a lot of computation time to consider the larger grids that would be needed to get closer to 2.)"
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]
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},
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{
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@@ -446,7 +378,7 @@
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{
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"data": {
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"text/plain": [
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"7.58150113722517"
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"7.037297677691766"
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]
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},
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"execution_count": 10,
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@@ -491,10 +423,10 @@
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{
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"data": {
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"text/plain": [
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"{'mean': 7.246114781372947,\n",
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" 'max': 7.716049382716049,\n",
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" 'min': 6.830601092896175,\n",
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" 'stdev': 0.181119344027548,\n",
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"{'mean': 7.239472697041692,\n",
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" 'max': 7.9239302694136295,\n",
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" 'min': 6.6711140760507,\n",
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" 'stdev': 0.19030622926154506,\n",
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" 'N': 200}"
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]
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},
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@@ -504,7 +436,7 @@
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},
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{
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"data": {
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"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 640x480 with 1 Axes>"
|
||||
]
|
||||
@@ -536,10 +468,10 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'mean': 7.402852321356604,\n",
|
||||
" 'max': 7.635044855888529,\n",
|
||||
" 'min': 7.126313914127917,\n",
|
||||
" 'stdev': 0.10047800378358163,\n",
|
||||
"{'mean': 7.4134560772843425,\n",
|
||||
" 'max': 7.651109410864575,\n",
|
||||
" 'min': 7.116171499733143,\n",
|
||||
" 'stdev': 0.10453350361308941,\n",
|
||||
" 'N': 200}"
|
||||
]
|
||||
},
|
||||
@@ -549,7 +481,7 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 640x480 with 1 Axes>"
|
||||
]
|
||||
@@ -571,10 +503,10 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'mean': 7.469780220918766,\n",
|
||||
" 'max': 7.719358435543357,\n",
|
||||
" 'min': 7.246960302761897,\n",
|
||||
" 'stdev': 0.06989052018543407,\n",
|
||||
"{'mean': 7.47612464655258,\n",
|
||||
" 'max': 7.681147051292993,\n",
|
||||
" 'min': 7.279786459597185,\n",
|
||||
" 'stdev': 0.07889928048753433,\n",
|
||||
" 'N': 200}"
|
||||
]
|
||||
},
|
||||
@@ -584,7 +516,7 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 640x480 with 1 Axes>"
|
||||
]
|
||||
@@ -602,7 +534,7 @@
|
||||
"id": "6d20f32a-8c7a-4456-aa41-d2989e33fd57",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"I think that what's happening is that the clusters that are near the edge of the grid get arbitrarily cut off, and since the edge is a smaller percentage of the larger grid, the larger grid has a larger mean cluster size, one that is a better representative of what would happen on an infinite grid. But I can't say what the mean converges to."
|
||||
"I think that what's happening is that the clusters that are near the edge of the grid get arbitrarily cut off, and since the edge is a smaller percentage of the larger grid, the larger grid has a larger mean cluster size, one that is a better representative of what would happen on an infinite grid. But I can't say exactly what the mean converges to."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -612,7 +544,7 @@
|
||||
"source": [
|
||||
"# My First Random Cluster\n",
|
||||
"\n",
|
||||
"The great thing about an *n* × 1 grid is that the clusters can't interfere with each other. Going left-to-right, once one cluster ends, the next one starts, and there's no looping back. But in an arbitrary 2D array there is looping back. So I want to get a feel for what the \"first\" cluster on an infinite grid looks like: start by placing the first color at the origin square, then recursively place random colors in neighboring squares, extending the cluster, but stop when the cluster is completely surrounded by squares of the second color. "
|
||||
"The great thing about an *n* × 1 grid is that the clusters can't interfere with each other. Going left-to-right, once one cluster ends, the next one starts, and there's no looping back. But in an arbitrary 2D array there is looping back. So I want to get a feel for what the \"first\" cluster on an infinite grid looks like: start by placing a color at the origin square, then recursively place random colors in neighboring squares, extending the cluster, but stop when the cluster is completely surrounded by squares of the other color. "
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -622,16 +554,15 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def random_cluster(colors='@.') -> Grid:\n",
|
||||
" \"\"\"Create just enough of a grid to cover a single random cluster of the first color.\"\"\"\n",
|
||||
" c = colors[0]\n",
|
||||
" cluster = {(0, 0): c}\n",
|
||||
" Q = neighbors((0, 0))\n",
|
||||
"def random_cluster(colors='@.', start=(0, 0)) -> Grid:\n",
|
||||
" \"\"\"Create just enough of a grid to create a single random cluster.\"\"\"\n",
|
||||
" cluster = {}\n",
|
||||
" Q = [start] # A queue of the frontier squares of the cluster\n",
|
||||
" while Q:\n",
|
||||
" sq = Q.pop()\n",
|
||||
" if sq not in cluster:\n",
|
||||
" cluster[sq] = random.choice(colors)\n",
|
||||
" if cluster[sq] == c:\n",
|
||||
" if cluster[sq] == cluster[start]:\n",
|
||||
" Q.extend(neighbors(sq))\n",
|
||||
" return cluster"
|
||||
]
|
||||
@@ -651,15 +582,17 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def show(cluster: Grid, color='@') -> int:\n",
|
||||
"def show(cluster: Grid) -> int:\n",
|
||||
" \"\"\"Print a representation of the grid and return the size of the one cluster.\"\"\"\n",
|
||||
" xs = sorted({x for (x, y) in cluster})\n",
|
||||
" ys = sorted({y for (x, y) in cluster})\n",
|
||||
" for y in ys:\n",
|
||||
" print(*[cluster.get((x, y), ' ') for x in xs])\n",
|
||||
" return cluster_size(cluster, color)\n",
|
||||
" return cluster_size(cluster)\n",
|
||||
"\n",
|
||||
"def cluster_size(cluster, color='@') -> int: return Counter(cluster.values())[color]"
|
||||
"def cluster_size(cluster) -> int: \n",
|
||||
" color = cluster[0, 0]\n",
|
||||
" return Counter(cluster.values())[color]"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -672,12 +605,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . \n",
|
||||
". @ . \n",
|
||||
". @ @ . . \n",
|
||||
" . @ @ @ .\n",
|
||||
" . @ . . \n",
|
||||
" . @ @ . \n",
|
||||
" . . \n",
|
||||
". @ @ .\n",
|
||||
". @ . \n",
|
||||
" . \n"
|
||||
@@ -686,7 +614,7 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"12"
|
||||
"3"
|
||||
]
|
||||
},
|
||||
"execution_count": 17,
|
||||
@@ -695,6 +623,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"random.seed(37)\n",
|
||||
"show(random_cluster())"
|
||||
]
|
||||
},
|
||||
@@ -708,30 +637,45 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . . . . \n",
|
||||
" . @ @ . . @ @ . \n",
|
||||
". @ @ @ @ @ @ @ @ . \n",
|
||||
" . @ @ . . @ . @ @ . \n",
|
||||
" . \n",
|
||||
" . @ . \n",
|
||||
" . @ @ . \n",
|
||||
" . . @ . \n",
|
||||
" . @ . . @ . \n",
|
||||
" . @ @ @ @ @ . \n",
|
||||
" . . @ @ . @ . @ .\n",
|
||||
" . . @ . @ @ @ @ @ @ @ .\n",
|
||||
" . @ . @ @ @ @ @ @ . . . \n",
|
||||
" . @ @ @ @ . . @ . \n",
|
||||
" . . @ . @ . @ . \n",
|
||||
" . . @ . . . @ @ @ @ . \n",
|
||||
" . . @ . . @ @ @ @ @ . . . \n",
|
||||
" . @ @ @ @ . . @ @ . @ @ @ . \n",
|
||||
" . @ @ @ . . . @ @ . @ @ . . \n",
|
||||
" . . @ @ @ @ @ @ . @ . @ . @ @ @ @ . \n",
|
||||
" . @ @ @ . . @ . @ @ @ @ . @ @ . . . \n",
|
||||
" . @ . @ . . . @ . @ @ @ @ @ . \n",
|
||||
" . . @ . . @ @ @ . . . . . \n",
|
||||
" . @ @ . @ @ . @ . \n",
|
||||
" . @ . @ @ @ . . \n",
|
||||
" . @ @ @ @ @ @ @ . \n",
|
||||
" . @ @ @ . @ @ @ . \n",
|
||||
" . . . . . @ @ @ . @ @ . \n",
|
||||
" . @ @ @ . . @ @ @ @ @ @ . @ . \n",
|
||||
" . @ @ @ . @ @ . . @ @ . . \n",
|
||||
" . @ @ @ @ @ @ . @ . \n",
|
||||
" . @ @ . . . . @ @ @ . \n",
|
||||
" . . . @ . . @ . \n",
|
||||
" . @ . . @ @ @ . @ . \n",
|
||||
" . @ . . @ @ . . \n",
|
||||
" . @ @ @ . @ @ . \n",
|
||||
" . @ @ @ @ . @ . \n",
|
||||
" . @ @ @ . @ . \n",
|
||||
" . @ @ . @ @ . \n",
|
||||
" . @ @ @ @ . \n",
|
||||
" . @ . @ . \n",
|
||||
" . @ @ . . \n",
|
||||
" . @ @ @ . @ .\n",
|
||||
" . . @ @ @ .\n",
|
||||
" . @ . . \n",
|
||||
" . \n"
|
||||
". @ @ . @ @ . . \n",
|
||||
" . @ @ @ . \n",
|
||||
" . @ @ @ . \n",
|
||||
" . . . \n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"61"
|
||||
"167"
|
||||
]
|
||||
},
|
||||
"execution_count": 18,
|
||||
@@ -753,29 +697,18 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . \n",
|
||||
" . @ . . . . \n",
|
||||
" . @ @ @ @ @ . \n",
|
||||
" . . @ @ . @ @ @ . \n",
|
||||
" . . @ @ @ @ . @ . . \n",
|
||||
" . @ . . @ . @ @ @ . \n",
|
||||
" . @ @ @ . . . @ @ . \n",
|
||||
" . @ @ . . @ . . . . . \n",
|
||||
" . . @ @ . . . . . @ . . @ @ @ @ .\n",
|
||||
" . . . @ @ @ . @ @ @ @ . . @ . . . . @ . . . \n",
|
||||
" . @ @ @ @ @ . . . . @ @ @ @ @ . @ @ @ @ @ . \n",
|
||||
". @ @ @ @ @ @ @ @ @ @ @ . . . @ . @ . @ @ . \n",
|
||||
" . @ @ @ . @ @ @ . @ . . @ @ @ @ @ . . \n",
|
||||
" . . @ . @ . . . . @ @ @ @ @ @ . \n",
|
||||
" . . . @ @ @ . . . . \n",
|
||||
" . . \n",
|
||||
". @ @ . . \n",
|
||||
" . . \n"
|
||||
" . @ @ @ .\n",
|
||||
" . . @ .\n",
|
||||
" . @ .\n",
|
||||
" . \n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"100"
|
||||
"7"
|
||||
]
|
||||
},
|
||||
"execution_count": 19,
|
||||
@@ -792,7 +725,7 @@
|
||||
"id": "faf079b0-8534-4d92-aa8e-acd035dc5420",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can see that there is a lof of variation in size and shape of the first clusters. We can also see that the shape will constrain other clusters: there are some small clusters of the second color that are trapped inside the cluster of the first color. Below I sample 10,000 first clusters and report on their sizes:"
|
||||
"We can see that there is a lot of variation in size and shape of the first clusters. We can also see that the shape will constrain other clusters: there are some small clusters of the second color that are trapped inside the cluster of the first color. Below I sample 10,000 first clusters and report on their sizes:"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -809,18 +742,12 @@
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"id": "df7f6ae0-32aa-4002-8056-9de0dc2da07a",
|
||||
"metadata": {
|
||||
"collapsed": true,
|
||||
"jupyter": {
|
||||
"outputs_hidden": true
|
||||
},
|
||||
"scrolled": true
|
||||
},
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'mean': 59.3772, 'max': 703, 'min': 1, 'stdev': 75.3564687329362, 'N': 10000}"
|
||||
"{'mean': 59.6728, 'max': 917, 'min': 1, 'stdev': 75.3054688022268, 'N': 10000}"
|
||||
]
|
||||
},
|
||||
"execution_count": 21,
|
||||
@@ -829,7 +756,7 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 640x480 with 1 Axes>"
|
||||
]
|
||||
@@ -853,13 +780,17 @@
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"id": "2f1dacba-d47c-46ab-be44-b5129e317ef4",
|
||||
"id": "3dcbff13-ddb1-4ba0-9650-3b6b6122f76a",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'mean': 11.6556, 'max': 32, 'min': 1, 'stdev': 9.159878236846971, 'N': 5000}"
|
||||
"{'mean': 7.851026539809714,\n",
|
||||
" 'max': 20,\n",
|
||||
" 'min': 1,\n",
|
||||
" 'stdev': 5.816812011424741,\n",
|
||||
" 'N': 3994}"
|
||||
]
|
||||
},
|
||||
"execution_count": 22,
|
||||
@@ -868,7 +799,7 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 640x480 with 1 Axes>"
|
||||
]
|
||||
@@ -878,7 +809,16 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"report(sorted(sizes)[:5000])"
|
||||
"smaller = [s for s in sizes if s <= 20]\n",
|
||||
"report(smaller, bins=range(22))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "e93bc126-d2c9-415d-97cf-ee07bd36502d",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We see that there are over 600 clusters of size 1. That makes sense; we start with one square, and about once every 2<sup>4</sup> times all 4 neighbors will be the other color, and 10000 / 16 = 625."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
Reference in new issue
Block a user