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4

Here is some code I used, which may partially answer your question. The key is to calculate efficiently points near the border of the Mandelbrot set. These points have large iteration counts which, when iterated, produce the Buddhabrot form. The algorithm linked to in the question uses an adaptive mesh of squares to locate border points. The alternate code ...


4

As this is special-functions question, I feel justified in using a bit of heavy artillery. Here goes nothing... In effect, what the OP seems to want to do is to evaluate $$\sum_{n=1}^\infty \frac{(q^{n+1};q)_\infty}{(q^n;q)_\infty} q^{n-1}$$ where $(a;q)_n$ is the $q$-Pochhammer symbol by approximating it with its partial sums. However, there is a more ...


11

Although this is hardly a debilitating bug I wondered what else might be affected so I decided to trace this further. I found that the bug affects TreeForm by way of TreePlot. Here is a reduced example of the call that originates in the exhibit above: TreePlot[{1 -> 2, 1 -> 3, 1 -> 4}, Top, 1, "VertexNames" -> {List, HoldForm["foo"], ...


5

Considering the use of the old utility MakePolygons[] by Roman Maeder, as well as the year Hanson's paper appeared, I believe this was done during the time one still had to load a package to be able to use ParametricPlot3D[]. Since ParametricPlot3D[] has been built-in for quite a while now, please allow me to present a modernized plot of the Fermat surface ...


18

This response defines a function called traceTypes which provides a quick-and-dirty visualization of type system operation. The function is somewhat fragile as it depends upon undocumented implementation details in version 10.2. Despite this fragility, it might be useful for study purposes as it handles many common type system use cases. The code for the ...


2

You don't need to write code to find cycles. There is a built-in function for that (FindCycle) Besides, using pattern matching for this goal as you did is bound to be rather slow. For visualization of the cycles you can use HighlightGraph. g = Graph[Rule @@@ a, VertexLabels -> "Name"] cycles = FindCycle[g, Infinity, 99999] Manipulate[ ...


5

A small change to the LabelingFunction seems to do the trick: BarChart[{{0.123, 0.492}, {2.865, 0.055}, {1.03, 1.084}, {4.282, 0.053}}, AxesLabel -> {"", "Value"}, ChartLabels -> {Placed[{"data1", "data2", "data3", "data4"}, {{0.5, 0}, {0.8, 1.2}}, Rotate[#, (1.75/7) Pi] &], Placed[{"", ""}, Above]}, LabelingFunction -> ( ...


1

Here's a somewhat different approach: With[{s = 101, (* resolution *) w = 2 (* thickness *)}, Block[{h = (s + 1)/2}, rules = {a1 -> Image[SparseArray[{{j_, k_} /; h - w <= j <= h + w || h - w <= k <= h + w :> 0}, {s, s}, 1]], a2 -> Image[SparseArray[{{j_, k_} ...



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