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345

I have to confess that I see this as a proper challenge, as I am usually quite creative in finding/combining functions to provide a desired behavior. So I will give it another try. which is generated using box[x_, x1_, x2_, a_, b_] := Tanh[a (x - x1)] + Tanh[-b (x - x2)]; ex[z_, z0_, s_] := Exp[-(z - z0)^2/s] and r[z_, x_] := (*body*).4 (1.0 - .4 ...


189

This might get me suspended from the site butt I cannot resist. The shape you are looking for can probably be approximated (depending how anal you want to be about the outcome) by two assymetric probability distributions. The obvious choices would be a Poasson or a log normal distribution. I will use the latter as it is continuous. Now the bummer is that ...


93

Parametric Buttocks Manipulator Manipulate[ ParametricPlot3D[{ (e u^p + (1 + (c - a u) (u - 1)) Cos[t]^2) Sin[t], (e u^p + (1 + (d - b u) (u - 1)) Cos[t]^2) Cos[t], 2 u}, {t, -0.2, Pi + 0.2}, {u, 0, 1.1}, Lighting -> "Neutral", Mesh -> None, PlotStyle -> Directive[Specularity[0], RGBColor[0.92, 0.85, 0.73]], Axes -> False], {{a, ...


47

If you want to make several sequences of the Collatz function for turning it into a graph, you probably want to memorize, which parts you already calculated. What we try to do is to create a graph like this (image from xkcd) When we would calculate the whole chain for each number until it (hopefully) reaches the end sequence 8,4,1 we do a lot of work over ...


46

In this answer, I will concentrate on the colors only to create something like this Copying the colors from python is a very fast way to get similar results. Nevertheless, the best way to understand what's happening is still to read the underlying publication that was used in seaborn: A colour scheme for the display of astronomical intensity images ...


34

Using color functions efficiently in data visualizations is more of an art than a recipe, so don't worry if you're not "good" at it yet. It's only a matter of time :) Copying the color schemes from seaborn: The best way to mimic those color schemes in Mathematica would be to copy the RGB values from seaborn for your preferred color scheme. You can find ...


33

Manipulate[ ParametricPlot[({Sin[n t1], Sin[(n - 1) t1]}), {t1, 0, 2 Pi}, Epilog -> {Red, PointSize[Large], Table[If[OddQ[i + j], Point[{Cos[Pi i/(2 (n - 1))], Cos[Pi j/(2 (n))]}]], {i, 2 n - 3}, {j, 2 n - 1}]}], {{n, 5}, 2, 20, 1}] General Case I We can generalize to the Lissajous curve specified by the two non-negative ...


29

Well, an unusual question to answer, what about something like this Plot3D[.7*(1 + Tanh[1 - (2*Y^2 + X^2 + X^4)]) - .3*Exp[-X^2/.0025]* Exp[-(Y - .1)^2/.15] - .2*(Exp[-(X - .7)^2/.02]*Exp[-(Y - .0)^2/.08] + Exp[-(X + .7)^2/.02]*Exp[-(Y - .0)^2/.08]), {X, -1, 1}, {Y, -1, 1}]


29

Styling closer to your example, using The Toad's colors: colors = {RGBColor[{0.9312692223325372, 0.8201921796082118, 0.7971480974663592}], RGBColor[{0.8822898168737189, 0.695820866705742, 0.7065457119485431}], RGBColor[{0.8135380254700676, 0.5705055182357822, 0.639280859468155}], RGBColor[{0.7195800708349119, 0.45537982893127477`, ...


29

This can be done more-or-less easily with a combination of options for AxesOrigin, PlotRange, and PlotRangePadding and the CustomTicks package (for easy outward-facing ticks). Needs["CustomTicks`"]; GapAxes[plot_Graphics, ticks : {{x__}, {y__}}, scalefactor_: Automatic] := With[ {prange = ticks[[All, 1 ;; 2]], s = Flatten@{scalefactor /. Automatic ...


28

This is the Collatz function I know: Collatz[1] := {1} Collatz[n_Integer] := Prepend[Collatz[3 n + 1], n] /; OddQ[n] && n > 0 Collatz[n_Integer] := Prepend[Collatz[n/2], n] /; EvenQ[n] && n > 0 Generating a graph from this is easy: Graph[(DirectedEdge @@@ Partition[Collatz[#], 2, 1]) & /@ Range[500] // Flatten // Union, ...


26

First define the Morse code (from rosettacode.org with corrections by @evanb) morsecode = (#1 -> Characters[#2]) & @@@ { {"a", ".-"}, {"b", "-..."}, {"c", "-.-."}, {"d", "-.."}, {"e", "."}, {"f", "..-."}, {"g", "--."}, {"h", "...."}, {"i", ".."}, {"j", ".---"}, {"k", "-.-"}, {"l", ".-.."}, {"m", "--"}, {"n", "-."}, {"o", "---"}, ...


26

Fortunately, Wikipedia has the answer, as long as we are content to restrict ourselves to non-intersecting closed polygons. This will probably be an acceptable limitation, given that excessively complicated plot markers tend to look slightly distracting anyway. Because we seek an aesthetic rather than rigorously well defined result, we do not need to be ...


25

Some function definitions first. AkimaInterpolation[] stolen from here (Thanks JM, wherever you are!): AkimaInterpolation[data_] := Module[{dy}, dy = #2/#1 & @@@ Differences[data]; Interpolation[Transpose[{List /@ data[[All, 1]], data[[All, -1]], With[{wp = Abs[#4 - #3], wm = Abs[#2 - #1]}, If[wp + wm == 0, (#2 + #3)/2, (wp #2 + wm ...


23

Based on Oleksandr's excellent design idea here is my reimplementation of his package which offers much richer set of shapes and is completely compatible with Oleksandr's. The package can be loaded and installed from GitHub: (* Load the package code *) package = Import["http://raw.github.com/AlexeyPopkov/PolygonPlotMarkers/master/PolygonPlotMarkers.m", ...


22

maybe this will provide a little insight: first look at the evaluation points used by ContourPlot: f[x_?NumericQ, y_?NumericQ] := (Sow[{x, y}]; Sin[3.2 x]*Sin[1.3*y] - 2.1*Sin[1.3*x]*Sin[3.2*y]); {plot, dat} = Reap[ContourPlot[f[x, y] == 0, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, ContourStyle -> Red]]; Row[{ ...


21

Your comment raises interesting question: I got everything simply faded and flat, while in the example - its all bright and sharp I think the problem is related to the fact that Mathematica's graphical functions always work in linear colorspace. Starting from Pickett's solution with better resampling method, in version 10.0.1 we obtain: ...


20

Graphics[{Circle[{0, 0}, 1, {0, Pi}], Circle[{0, 0}, .03], Line[{{1, 0}, {1, -.1}, {-1, -.1}, {-1, 0}}], Rotate[ Line[{{.03, 0}, {.6, 0}}] , #, {0, 0}] & /@ {0, Pi/2, Pi}, GeometricTransformation[ Piecewise[{ {{Red, Line[{{.8, 0}, {1, 0}}], Black, Line[{{.2, 0}, {.5, 0}}], Rotate[{Red, Text[#, {.75, 0}, {0, ...


19

I wrote the ColorBar package exactly for this purpose and it makes such modifications easy. The README.m should give you all the instructions you need, but I'll summarize it here. After installing the package (copy ColorBar.m to FileNameJoin[{$UserBaseDirectory, "Applications"}]), do the following: ColorBar["TemperatureMap"] Now you can click on the ...


19

Method 1: FindCurvePath (as mentioned by Yves Klett). This method is simple, but unfortunately, there are small issues (as shown in plots), that the curves are not identified perfectly. arrayData = Flatten[Function[{lst}, {First @ lst, #} & /@ Rest[lst]] /@ originalData, 1]; curvesPosition = FindCurvePath[arrayData]; ListPlot[curves = ...


19

If you are comfortable using undocumented and unsupported functionality we can do this with a ScalingFunctions option as I did for ListLogLinearPlot for the whole real numbers. (* listability *) (self : fn[off_, scale_])[x_List] := self /@ x (self : invfn[off_, scale_])[x_List] := self /@ x fn[off_, scale_][x_?NumericQ] := If[x < off, Log[x], ...


18

You can make plots sort of like this: Or this: Or this: ...by taking advantage of Image and Fourier using the following code. The plots will have a brightness proportional to the multiplicity of the root, and you can change the colors, convolution properties, etc., although it doesn't provide axes (you'll have to figure that out yourself). ...


18

To long for a comment, but here's one approach, using information readily available in the docs and on this site: First, make a map that wraps a globe changing the Geoprojection to something a bit more useful. img = With[{Δ = 30}, Row[Table[ GeoGraphics[GeoBackground -> GeoStyling["ReliefMap"], GeoRange -> {{-90, 90}, {λ, λ + Δ}}, ...


18

Update ticks[x1_, x2_] := {#/10 + π/2, #} & /@ FindDivisions[{10 (x1 - π), 10 (x2 - π)}, 20] funcs = Table[3 + BesselJ[i, 10 (x -π/2)], {i, 0, 3}]; PolarPlot[funcs // Evaluate, {x, -π/2, 3π/2}, PolarAxes -> Automatic, PolarTicks -> {ticks[0, 2 π][[2 ;; -2]], Automatic} ] (*thanks @kguler 's and @rm-rf 's advice*) Manipulate ...


18

A crude attempt This is for Mathematica 10+ only. To construct each face, I use an intersection between a unit 3-ball centred at the origin and a pyramid whose base is at infinity and apex is at the origin. Each edge of the pyramid passes through each vertex of the spherical face. The pyramid is given by ConicHullRegion[{origin}, {vertices}]. The ...


18

Ok, here's a very brief toy example while I don't have access to my desktop computer at work. It's easy enough to figure out, that a LogPlot of f is basically the plot of Log[f[x]]. And A LogLinearPlot is the plot of f[Exp[x]]. But we can extend this to arbitrary scalings of the axes. I start with defining a piecewise function which maps x values between 0 ...


18

You can use your ContourPlot, you just need to wrap coordinates with GeoPosition, note that you have to flip order. (if x is longitude and y is latitude, because GeoPosition assumes first is latitude and so on.) cp is Graphics[GraphicsComplex[coordinates, primitives]...], it is convenient to use this form. We can apply GeoPosition in one place and reduce ...


18

Quick&Dirty: pt = {0, 0}; full = MandelbrotSetPlot[]; r = 0.2; Column[{ Row[{"Zoom: ", Slider[Dynamic[r], {0.01, 1}]}], Row[ { LocatorPane[Dynamic[pt], Dynamic[Show[full, Graphics[{EdgeForm[Red], Transparent, Rectangle[pt + r, pt - r]}], ImageSize -> Scaled[.45]]]], Dynamic[ MandelbrotSetPlot[{pt + r, ...


18

I think SmoothDensityHistogram (docs here) is what you are looking for: data1 = RandomVariate[BinormalDistribution[{0, 0}, {2, 3}, 0.5], 100000]; data2 = RandomVariate[BinormalDistribution[{3, 4}, {2, 2}, .1], 100000]; data = data1~Join~data2; This is just some random sample data. If you plot it using ListPlot, you obtain the "blob" you mentioned: ...


17

RegionFunction is the option you are looking for. ContourPlot[ Evaluate[Sum[Sin[RandomReal[5, 2].{x, y}], {5}]], {x, -3, 3}, {y, -3, 3}, BoundaryStyle -> {Thick, Black}, RegionFunction -> Function[{x, y, z}, x^2 + y^2 < 9] ]



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