### 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 maximumÂ lengthÂ 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:

**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