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30

Let you have a function and an initial point f[x_] := Cos[x] x0 = 0.2; Then you can calculate a sequence seq = NestList[f, x0, 10] (* {0.2, 0.980067, 0.556967, 0.848862, 0.660838, 0.789478, \ 0.704216, 0.76212, 0.723374, 0.749577, 0.731977} *) and vizualize it with a so-called Cobweb plot p = Join @@ ({{#, #}, {##}} & @@@ Partition[seq, 2, 1]); ...


7

dottie = FindRoot[Cos[x] == x, {x, 1}] // Values // First 0.739085 Plot[{Cos[x], x}, {x, -5, 5}, Epilog -> {Red, PointSize[0.02], Point[{dottie, dottie}]}] Convergence can be seen with EvaluationMonitor {res, {evx}} = Reap[FindRoot[Cos[x] == x, {x, 0}, EvaluationMonitor :> Sow[x]]] {{x -> 0.739085}, {{0., 1., 0.750364, 0.739113, ...


3

Needs["MultivariateStatistics`"] data = Table[RandomVariate[BinormalDistribution[{50, 50}, {5, 7}, .8]], {1000}]; Show[ ListPlot[data, Epilog -> { Text[Framed["1.00", Background -> LightBlue], {45, 25}], Text[Framed["0.98", Background -> LightBlue], {50, 33}], Text[Framed["0.90", Background -> LightBlue], {55, 43}] }, ...


2

There are couple other ways to visualize 3D images, one of which is new in V10. (Note: The links to the original data are no longer valid.) The new features, ClipPlanes and IntervalSlider, are useful here. Something like this was demonstrated at WTC 2014. knee = Raster3D[ RawArray["Byte", ImageData[ExampleData[{"TestImage3D", "MRknee"}], ...


1

Two slight improvements to the code: [1] Using Function is faster: f[α_] = Function[x, α x (1 - x)]; [2] One should localise seq, and Riffle is clearer than Join @@ ({{#, #}, {##}} & @@@ logistic[α_, x0_] := Module[{seq}, seq = NestList[f[α], x0, 100]; p = Riffle[Transpose[{seq, seq}], Partition[seq, 2, 1]]; Plot[{f[α]][x], x}, {x, 0, ...


1

Sometimes, the file size and number of frames of a bvh file can be very large, one might skip every other frames to reduce the file size and cut half of the number of frames. The example below, has 3602 frames and 2,559KB in size, one can cut it into half with the following codes: srcFile = "https://www.dropbox.com/s/j4k5f4vfqb592tw/Dance01.bvh?dl=1"; ...



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