# Updating ParametricPlot3D code from Getz and Helmstedt book to use V10.3 features

I purchased a version of Graphics with Mathematica, Fractals, Julia Sets, Patterns and Natural Forms, by Chonta Getz and Janet Helmstedt, written in 2004. Really fun book.

I’m looking at the following code.

ParametricPlot3D[
{(9 Cos[Î¸] – Cos[9 Î¸]) Cos[t] – 5 t,
(9 Sin[Î¸] – Sin[9 Î¸]) Cos[t] – 7 t,
7 t,
RGBColor[0.52 + Abs[t/(2 Ï€)], 0.8 – Abs[t/(2 Ï€)], 0.54]},
{t, -Ï€/2, Ï€/2}, {Î¸, 0, 2 Ï€},
AspectRatio -> Automatic,
PlotPoints -> 50,
ViewPoint -> {2.870, 1.385, 1.137},
Axes -> False,
Boxed -> False,
Lighting -> False]

Now, this was back in the day when ParametricPlot3D did not have a PlotStyle option. Of course, this code will not work in the latest version of Mathematica 10.3.0.0, but I am wondering how I would repair it to get their image, which looks like this:

I am enjoying their discussion and use of color, so what I am looking for in this question is how to employ their color intent in the latest version of Mathematica.

=================

2

If you want to experience the old system: < (
RGBColor[0.52 + Abs[#4/(2 Ï€)],
0.8 – Abs[#4/(2 Ï€)], 0.54] &),
AspectRatio -> Automatic,
PlotPoints -> 50,
ViewPoint -> {2.870, 1.385, 1.137},
Axes -> False,
Boxed -> False,
Background -> ColorData[“CoffeeTones”][.9]]

Am I correct in thinking that #1, #2, and #3 refer to x, y, and z, and since the first parameter is t, that’s #4? And #5 would correspond with θ\theta?
– David
Dec 14 ’15 at 18:16

@David – yes you are correct. This is covered in the documentation for ColorFunction.
– Bob Hanlon
Dec 14 ’15 at 22:05

Removing the RGBColor stuff in there, and fixing the Lighting option, made it work:

ParametricPlot3D[{
(9 Cos[\[Theta]] – Cos[9 \[Theta]]) Cos[t] – 5 t,
(9 Sin[\[Theta]] – Sin[9 \[Theta]]) Cos[t] – 7 t,
7 t},
{t, -\[Pi]/2, \[Pi]/2}, {\[Theta], 0, 2 \[Pi]},
AspectRatio -> Automatic,
Axes -> False,
Boxed -> False,
PlotPoints -> 50, ViewPoint -> {2.870, 1.385, 1.137},
Lighting -> Automatic]