Rose Voronoi and Lorenz Attractor Designs
by rbatzer
I made paper lace using a Voronoi diagram generated with a polar rose and a 2D graph of a Lorenz Attractor.
The polar rose is a the forms generated by the equation r= a*cos(theta*n/d) and results in the possible forms shown below (from Wikipedia). I chose this equation because it produces a large range of shapes from a single code.
I inserted this equation in the the “Random” Voronoi generator by Jennifer. My code is below, but not properly commented.
void setup() {
size(600,600,P3D); //size of your intended pattern
noLoop(); // don’t need to use the draw loop
/*unique name for your file. if left unchanged,
will simply save file with current milisecond*/
String fileName= “voronoi”+millis()+”.pdf”;
beginRaw(PDF, fileName); //enables you to save your design to a pdf
setupVoronoi(); // create your voronoi generator
int petalLength = 250; // variable to control the maximum length of each petal
float n=.232; //this is n/d and determines the petal shape
int numPoints=100; //number of points plotted.
float theta = 0;
float r=0;
float x=0;
float y=0;
//this will draw one spiral
for (int k=1;k<numPoints;k++) {
theta = 2*3.14159/numPoints*k;//change first number to decide how many times around the circle are plotted.
r=petalLength*cos(n*theta);
x=r*cos(theta)+300;
y=r*sin(theta)+300;
voronoi.addPoint(new Vec2D(x,y));
}
drawVoronoi(); //renders your voronoi
endRaw(); //ends the recording
Several generated images:
![](https://lh4.googleusercontent.com/-TjCOLtNlDrs/T2iqettNWfI/AAAAAAAABVY/ngDvO2Ibews/w387-h389-k/Untitled2.png)
![](https://lh6.googleusercontent.com/-z9ETrouL31U/T2iqe892rbI/AAAAAAAABVc/OY5tGnKN4vY/w411-h413-k/Untitled21.png)
![](https://lh4.googleusercontent.com/-8bssjqS8xEQ/T2iqe47wGEI/AAAAAAAABVg/Sxo5_MUILe0/w413-h414-k/Untitled245.png)
![](https://lh5.googleusercontent.com/-ZOM9czd1c4M/T2iqgPtUBKI/AAAAAAAABVk/NiyfMSqEqD0/s368-c-k/Untitled5.png)
![](https://lh6.googleusercontent.com/-ht4y2AL2XsE/T2iqgEW5k1I/AAAAAAAABVo/ayeICVzTpgk/w266-h266-n-k/fig1.jpg)
![](https://lh6.googleusercontent.com/-3yl5mI3hPJ8/T2iqg1_GMwI/AAAAAAAABVs/Xli1fBH_39A/w402-h401-k/fig2.png)
![](https://lh4.googleusercontent.com/-WXXe0r7obHE/T2iqhKO3C7I/AAAAAAAABVw/UC4gYteCYfg/w365-h368-k/fig3.png)
Resulting Lace:
My second interest is in using a Lorenz Attatractor to generate interesting shapes. Lorenze is a chaotic system that generates spirals on two planes. I used Matlab code I found online to produce the following images. All are from the same 3D plot shown from different directions.
Lace for one view