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10

Here's a metapost solution. bloomgrapha(m,n,s,u) draws the grid version. m and n are as in the question, s determines label scale, and u determines graph scale. bloomgraphb(m,n,d,s,u) as above draws the "bloom" version. Here m=layers, n=petals per layer. The additional argument d determines how far the petals extend. draw bloomgrapha(4,8,.75,7mm); ...

4

This is just to mention two things. One only needs one nested loop to draw this. (OK, several \ifnums, but still.) As mentioned in the paper, these are always the same graphs. That is, one can use the same algorithm but use different coordinate systems to draw the graph. This answer illustrates the point in three coordinate systems: Cartesian Polar ...

3

I guess this is not a real cylinder but a cylinder with an elliptical base. If you only need this one, you can use this code and yscale=0.5. \documentclass[tikz,border=3mm]{standalone} \usepackage{tikz-3dplot} \tikzset{declare function={ vcrity(\ph,\th)=atan2(sin(\th)*sin(\ph),min(cos(\ph),-1/sqrt(2))*cos(\th));% critical t value y cylinder vcritz(\ph,\th)=...

3

One possible solution is to use shapes.geometric library. Using this library, cylinder is easily obtained. \documentclass[border=5pt]{standalone} \usepackage{tikz,tikz-3dplot} \usetikzlibrary{shapes.geometric} \begin{document} \tdplotsetmaincoords{70}{30} \begin{tikzpicture}[tdplot_main_coords] \draw[->] (0,3,0) -- (0,-3,0) node[above] {$x$}; \draw[-...

2

This questions seems to be a follow-up of Using Lua functions with mplib and mpgraph You can simply construct the function that you want to plot from the macro parameter. \documentclass{article} \usepackage{luamplib} \directlua{userdata = userdata or {}} \begin{document} \def\plot#1{% \directlua{ function userdata.f(x) local _ENV = math ...

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