In my search to understand the creation of a guilloche and in relation to my post Recreating a guilloche with TikZ, I came about the code below,
Guilloche[a_, b_, c_, d_, e_, f_] :=
PolarPlot[Evaluate[Flatten[{ Table[(c + Sin[a x + d]) + ((b + Sin[b x + e]) - (c + Sin[a x + d]))(f + Sin[a x + n/ Pi])/2, {n, 0, 19}] }] ], {x, 0, 2 Pi}, PlotPoints -> 200, Axes -> None, Frame -> False]
Guilloche[4, 8, 20, 4.7, 1.8, 1];
Written in Mathematica which should produce the following image:
My attempt below compiles but with no image.
\documentclass[11pt]{scrartcl}
\usepackage[dvipsnames]{xcolor}
\usepackage{tkz-fct}
\begin{document}
\noindent\begin{tikzpicture}
\foreach \i in {1,...,19}{%
\tkzFctPolar[color=MidnightBlue,thick,domain=0:2*pi,samples=400]{(4 + sin(4*t + 4.7)) +((8 + sin(8*t + 1.8)) - (20 + sin(4*t + 4.7)))
(1 + sin(4*t + \i/ Pi))/2}}
\end{tikzpicture}
\end{document}
Any assistance on how to convert the code appropriately will be highly appreciated. In general, the Mathematica code should produce different guilloches but I don't know how I would be able to implement it into TikZ
to generate different guilloches from one piece of code.
Best Answer
It's a problem of units. You can use mathematica or excel or maxima or a free soft to calculate some values. After it's easy to find how to setup
\tkzInit
. Perhaps it's more easy with pgfplots.