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326.688}, {283.375, 247}} -> {-19.4049, -1.58039, 0.062901, 0.062901}, {{330.313, 366.75}, {283.375, 247}} -> {-21.923, -1.58039, 0.062901, 0.062901}, {{370.375, 406.75}, {283.375, 247}} -> {-24.441, -1.58039, 0.062901, 0.062901}, {{10.1875, 46.5625}, { 243.375, 207}} -> {-1.78481, -4.09643, 0.062901, 0.062901}, {{50.25, 86.625}, {243.375, 207}} -> {-4.30478, -4.09643, 0.062901, 0.062901}, {{ 90.25, 126.625}, {243.375, 207}} -> {-6.82082, -4.09643, 0.062901, 0.062901}, {{130.25, 166.625}, {243.375, 207}} -> {-9.33686, -4.09643, 0.062901, 0.062901}, {{170.25, 206.625}, {243.375, 207}} -> {-11.8529, -4.09643, 0.062901, 0.062901}, {{210.313, 246.688}, {243.375, 207}} -> {-14.3729, -4.09643, 0.062901, 0.062901}, {{250.313, 286.688}, {243.375, 207}} -> {-16.8889, -4.09643, 0.062901, 0.062901}, {{290.313, 326.688}, { 243.375, 207}} -> {-19.4049, -4.09643, 0.062901, 0.062901}, {{330.313, 366.75}, {243.375, 207}} -> {-21.923, -4.09643, 0.062901, 0.062901}, {{ 370.375, 406.75}, {243.375, 207}} -> {-24.441, -4.09643, 0.062901, 0.062901}, {{10.1875, 46.5625}, {203.313, 166.938}} -> {-1.78481, -6.61639, 0.062901, 0.062901}, {{50.25, 86.625}, {203.313, 166.938}} -> {-4.30478, -6.61639, 0.062901, 0.062901}, {{90.25, 126.625}, {203.313, 166.938}} -> {-6.82082, -6.61639, 0.062901, 0.062901}, {{130.25, 166.625}, {203.313, 166.938}} -> {-9.33686, -6.61639, 0.062901, 0.062901}, {{170.25, 206.625}, { 203.313, 166.938}} -> {-11.8529, -6.61639, 0.062901, 0.062901}, {{210.313, 246.688}, {203.313, 166.938}} -> {-14.3729, -6.61639, 0.062901, 0.062901}, {{250.313, 286.688}, {203.313, 166.938}} -> {-16.8889, -6.61639, 0.062901, 0.062901}, {{290.313, 326.688}, {203.313, 166.938}} -> {-19.4049, -6.61639, 0.062901, 0.062901}, {{330.313, 366.75}, {203.313, 166.938}} -> {-21.923, -6.61639, 0.062901, 0.062901}, {{370.375, 406.75}, {203.313, 166.938}} -> {-24.441, -6.61639, 0.062901, 0.062901}, {{10.1875, 46.5625}, {163.313, 126.938}} -> {-1.78481, -9.13243, 0.062901, 0.062901}, {{50.25, 86.625}, { 163.313, 126.938}} -> {-4.30478, -9.13243, 0.062901, 0.062901}, {{90.25, 126.625}, {163.313, 126.938}} -> {-6.82082, -9.13243, 0.062901, 0.062901}, {{130.25, 166.625}, {163.313, 126.938}} -> {-9.33686, -9.13243, 0.062901, 0.062901}, {{170.25, 206.625}, {163.313, 126.938}} -> {-11.8529, -9.13243, 0.062901, 0.062901}, {{210.313, 246.688}, {163.313, 126.938}} -> {-14.3729, -9.13243, 0.062901, 0.062901}, {{250.313, 286.688}, {163.313, 126.938}} -> {-16.8889, -9.13243, 0.062901, 0.062901}, {{290.313, 326.688}, {163.313, 126.938}} -> {-19.4049, -9.13243, 0.062901, 0.062901}, {{330.313, 366.75}, { 163.313, 126.938}} -> {-21.923, -9.13243, 0.062901, 0.062901}, {{370.375, 406.75}, {163.313, 126.938}} -> {-24.441, -9.13243, 0.062901, 0.062901}, {{ 10.1875, 46.5625}, {123.313, 86.9375}} -> {-1.78481, -11.6485, 0.062901, 0.062901}, {{50.25, 86.625}, {123.313, 86.9375}} -> {-4.30478, -11.6485, 0.062901, 0.062901}, {{90.25, 126.625}, {123.313, 86.9375}} -> {-6.82082, -11.6485, 0.062901, 0.062901}, {{130.25, 166.625}, {123.313, 86.9375}} -> {-9.33686, -11.6485, 0.062901, 0.062901}, {{170.25, 206.625}, {123.313, 86.9375}} -> {-11.8529, -11.6485, 0.062901, 0.062901}, {{210.313, 246.688}, {123.313, 86.9375}} -> {-14.3729, -11.6485, 0.062901, 0.062901}, {{250.313, 286.688}, {123.313, 86.9375}} -> {-16.8889, -11.6485, 0.062901, 0.062901}, {{290.313, 326.688}, {123.313, 86.9375}} -> {-19.4049, -11.6485, 0.062901, 0.062901}, {{330.313, 366.75}, {123.313, 86.9375}} -> {-21.923, -11.6485, 0.062901, 0.062901}, {{370.375, 406.75}, {123.313, 86.9375}} -> {-24.441, -11.6485, 0.062901, 0.062901}, {{10.1875, 46.5625}, {83.3125, 46.875}} -> {-1.78481, -14.1665, 0.062901, 0.062901}, {{50.25, 86.625}, {83.3125, 46.875}} -> {-4.30478, -14.1665, 0.062901, 0.062901}, {{90.25, 126.625}, { 83.3125, 46.875}} -> {-6.82082, -14.1665, 0.062901, 0.062901}, {{130.25, 166.625}, {83.3125, 46.875}} -> {-9.33686, -14.1665, 0.062901, 0.062901}, {{ 170.25, 206.625}, {83.3125, 46.875}} -> {-11.8529, -14.1665, 0.062901, 0.062901}, {{210.313, 246.688}, {83.3125, 46.875}} -> {-14.3729, -14.1665, 0.062901, 0.062901}, {{250.313, 286.688}, {83.3125, 46.875}} -> {-16.8889, -14.1665, 0.062901, 0.062901}, {{290.313, 326.688}, {83.3125, 46.875}} -> {-19.4049, -14.1665, 0.062901, 0.062901}, {{330.313, 366.75}, {83.3125, 46.875}} -> {-21.8853, -14.1422, 0.0627931, 0.0627931}, {{370.375, 406.75}, {83.3125, 46.875}} -> {-24.441, -14.1665, 0.062901, 0.062901}, {{10.1875, 46.5625}, {43.25, 6.875}} -> {-1.78481, -16.6845, 0.062901, 0.062901}, {{ 50.25, 86.625}, {43.25, 6.875}} -> {-4.30478, -16.6845, 0.062901, 0.062901}, {{90.25, 126.625}, {43.25, 6.875}} -> {-6.82082, -16.6845, 0.062901, 0.062901}, {{130.25, 166.625}, {43.25, 6.875}} -> {-9.33686, -16.6845, 0.062901, 0.062901}, {{170.25, 206.625}, {43.25, 6.875}} -> {-11.8529, -16.6845, 0.062901, 0.062901}, {{210.313, 246.688}, {43.25, 6.875}} -> {-14.3729, -16.6845, 0.062901, 0.062901}, {{250.313, 286.688}, {43.25, 6.875}} -> {-16.8889, -16.6845, 0.062901, 0.062901}, {{290.313, 326.688}, { 43.25, 6.875}} -> {-19.4049, -16.6845, 0.062901, 0.062901}, {{330.313, 366.75}, {43.25, 6.875}} -> {-21.923, -16.6845, 0.062901, 0.062901}, {{ 370.375, 406.75}, {43.25, 6.875}} -> {-24.441, -16.6845, 0.062901, 0.062901}}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Moving Averages", "Section"], Cell["Definition", "Commentary"], Cell[BoxData[ \(MovingAverage[data_List, n_Integer?Positive] := Drop[Plus@@NestList[RotateRight, data, n - 1], n - 1]\/n\)], "Input"], Cell["Numerical example", "Commentary"], Cell[CellGroupData[{ Cell[BoxData[ \(MovingAverage[\ {1., 2., 3., 4., 5., 6.}, 2]\)], "Input"], Cell[BoxData[ \({1.5`, 2.5`, 3.5`, 4.5`, 5.5`}\)], "Output"] }, Open ]], Cell["Symbolic example", "Commentary"], Cell[CellGroupData[{ Cell[BoxData[ \(MovingAverage[\ {a, b, c, d, e, f, g}, 5]\)], "Input"], Cell[BoxData[ \({1\/5\ \((a + b + c + d + e)\), 1\/5\ \((b + c + d + e + f)\), 1\/5\ \((c + d + e + f + g)\)}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Game of Life ", "Section"], Cell["\<\ Direct definition, operating on an array of black and white squares\ \ \>", "Commentary"], Cell[BoxData[ \(LifeStepArray[a_List] := MapThread[If[#1 == 1 && #2 == 4 || #2 == 3, 1, 0] &, {a, \[Sum]\+\(i = \(-1\)\)\%1\(\[Sum]\+\(j = \(-1\)\)\%1 RotateLeft[ a, {i, j}]\)}, 2]\)], "Input"], Cell["\<\ Optimized definition, operating on a list of positions of black \ squares\ \>", "Commentary"], Cell[BoxData[ \(\(\[ScriptCapitalN] = Flatten[Array[List, {3, 3}, \(-1\)], 1]; \)\)], "Input"], Cell[BoxData[ \(LifeStep[pos_] := With[{u = Split[Sort[Flatten[Outer[Plus, pos, \[ScriptCapitalN], 1], 1]]]}, Cases[u, {x_, _, _} \[Rule] x] \[Union] Cases[u, {x_, _, _, _} \[Rule] x] \[Intersection] pos]\)], "Input"], Cell["Here are the initial coordinates of the glider gun structure", "Commentary"], Cell[BoxData[ \(\(ggun = {{1, \(-13\)}, {2, \(-12\)}, {2, \(-13\)}, {3, \(-12\)}, {3, \(-14\)}, {4, \(-23\)}, {5, \(-22\)}, {5, \(-24\)}, {6, \(-11\)}, { 6, \(-20\)}, {6, \(-21\)}, {6, \(-25\)}, {6, \(-35\)}, {6, \(-36\)}, {7, \(-11\)}, {7, \(-12\)}, {7, \(-13\)}, {7, \(-14\)}, { 7, \(-20\)}, {7, \(-21\)}, {7, \(-25\)}, {7, \(-35\)}, {7, \(-36\)}, {8, \(-1\)}, {8, \(-2\)}, {8, \(-12\)}, {8, \(-13\)}, {8, \(-14\)}, {8, \(-15\)}, {8, \(-20\)}, {8, \(-21\)}, {8, \(-25\)}, { 9, \(-1\)}, {9, \(-2\)}, {9, \(-12\)}, {9, \(-15\)}, {9, \(-22\)}, { 9, \(-24\)}, {10, \(-6\)}, {10, \(-12\)}, {10, \(-13\)}, {10, \(-14\)}, {10, \(-15\)}, {10, \(-23\)}, {11, \(-6\)}, {11, \(-11\)}, {11, \(-12\)}, {11, \(-13\)}, {11, \(-14\)}, {12, \(-11\)}}; \)\)], "Input", AspectRatioFixed->True, FontFamily->"Courier", FontSize->11], Cell["This runs 10 steps in the evolution of the glider gun", "Commentary"], Cell[BoxData[ \(\(MapIndexed[Cuboid[Flatten[{#1, \ First[#2]}]]&, NestList[LifeStep, ggun, 10], \ {2}]; \)\)], "Input"], Cell["This displays the evolution in 3D", "Commentary"], Cell[CellGroupData[{ Cell[BoxData[ 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