Curlicue Fractals

[#1]

Here is a fun example, if you like math. You have probably heard of fractals. There are many fractal sets today. One of these sets is called curlicue fractals. You can learn more about them in this MathWorld article. The article uses Mathematica and the Wolfram Language, which have many dedicated functions for lots of math, but you can build your own fractal demonstration in a JMP data table:

The θ and φ data columns use formulas to generate the recursive fractal angles. The formulas depend on a constant s, which is defined as a table variable so that you can easily view and change it. The constant s is initially equal to π, but you can change it to other famous mathematical and physical constants or any value that you like.

The distance between points is always 1.

The x and y data columns perform the conversion from polar to rectangular coordinates and apply the recursion relation. This version, like the article, uses 10,000 recursions, but you can use more or less recursions to change the shape.

Use the Curlicue Fractal table script to launch Graph Builder and visualize the fractal.

Note that if you change the value of the table variable, the formulas run to update the data columns. This change is automatically pushed to Graph Builder to make a new plot.

[#2]

Nice! This makes it easier to change the value of the table variable and see the effect:

NamesDefaultToHere(1);

dt = DataTable("Curlicue Fractal.jmp");
sVal = dt << getTableVariable("s");

NewWindow("Curlicue Fractal Control",
	PanelBox("Move the slider to update the fractal",
		SliderBox(pi() - 0.3, pi() + 0.3, sVal, sliderScript);
		);
	);
	
sliderScript =
Expr(
	STV = Expr(dt << setTableVariable("s", sValTBD));
	SubstituteInto(STV, Expr(sValTBD), sVal);
	STV;
	);

[#3]

Very Cool!