For another submission to Viz as Art contest at Tableau, I wanted to create something involving randomness and random walk specifically. But I found that the classic random walk algorithm creates results that are, well…too random, as opposed to the organic, botanical shapes I was looking for. Luckily, someone has already thought of developing a “Random Walk with Transition Probabilities that Depend on Direction of Motion”. It sounds nerdy, but that is just the recipe that Mother Nature uses to build branches on a blueberry bush, dandelion’s see head or the maple tree outside my window. In particular, a particle always moves forward and changes direction or stays the course dependent on a given probability. One of the chapters in Clifford Pickover’s book “Computers, Pattern, Chaos and Beauty” describes this in more detail.

As with Lorenz Attractor visualization, I wrote a program in Processing to generate the points and export them to a text file. Below is a complete listing of the code:

[code language=”java”]

PrintWriter textFile;

//number of branches

int branchNum = 200;

//scale factor for angle theta

float delTheta = .9;

//scale factor for radius

float delRadius = 0.05;

//probability of transmission

float pt = 0.2;

//number of steps

int stepNum = 150;

//direction angle

float Theta = 0;

void setup(){

size(1000,1000);

background(0);

//initialize output text file

//textFile = createWriter(“txtfiles/points.txt”);

for (int branch = 0; branch < branchNum; branch++) {

//set initial conditions for each branch

float x0 = width/2;

float y0 = height/2;

float radius = 1;

float res = 0;

float dir = 1;

float lastDir = 1;

float thresh = 0;

strokeWeight(0);

stroke(0);

fill(random(1,255), random(1,255), random(1,255));

//stroke(random(1,255), random(1,255), random(1,255));

for (int step = 0; step < stepNum; step++) {

if (step == 0) {

res = random(0,1);

if (res > 0.5) {

dir=1;

} else {

dir=-1;

}

res = res * dir;

Theta = Theta + (res * delTheta);

radius = radius + delRadius;

float x = radius * cos(Theta) + x0;

float y = radius * sin(Theta) + y0;

line(x0, y0, x, y);

x0 = x;

y0 = y;

lastDir = dir;

} else {

if(lastDir == -1) {

thresh = pt;

} else {

thresh = 1 – pt;

}

res = random(0,1);

if (res > thresh) {

dir = 1;

} else {

dir = -1;

}

res = res * dir;

Theta = Theta + (res * delTheta);

radius = radius + delRadius;

float x = radius * cos(Theta) + x0;

float y = radius * sin(Theta) + y0;

line(x0, y0, x, y);

ellipse(x,y,10,10);

x0 = x;

y0 = y;

lastDir = dir;

//save output to text file

//textFile.println(branch + “,” + x + “,” + y);

//textFile.flush();

//exit();

}

}

}

}

[/code]

Just by changing one or two parameters, one can create an infinite number of patterns, some more organic looking than others. Here are sample outputs from Processing:

I imported the points into Tableau and played with different shapes, sizes an colours to achieve the best look. In the end, I settled for a basic grey circle with white outline. At first the monochrome chart was an uninteresting jumble of random points but after I added Branch field (unique branch number) to the Level of Detail, all tendrils got nicely separated revealing their organic structure.

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