Emergent Doodles

Skills: Emergence

I have always been fascinated by how simple rules can give rise to complex patterns. I first began exploring this idea on paper. I drew lines that adhered to specific rules (take 1 step, turn right, turn left). When the line encountered an obstacle (itself or the edge of the paper), it followed a different set of rules. Here are some patterns that I generated along with the rules that generated them.

Rule: Take 1 Step, Turn Right If !Right Go Straight
Rule: Take 1 Step, Turn Right, If !Right - turn left, If !left - stop
Rule: Take 3 steps, Turn right, If !right go diagonally
Rule: Take 2 Steps, Turn right, If ! then (Turn Left, Take 1 Step, Turn right)
Rule: Take 3 Steps, Turn right, Take 2 Steps, Turn right, Take 1 Step, Turn right, If !Right (Take 3 Steps, Turn left, Take 2 Steps, Turn left, Take 1 Step, Turn left)
Rule: Take 1 Step, Turn Right, Take 1 Step, Turn Right, Take 1 Step, Turn Left, Take 1 Step, Turn Left, If Obstacle go Straight
Rule: Take 1 Step, Turn right, If !right,(Turn left, Take 10 steps)
Rule: Take 3 Steps, Turn right, If !right turn left
Rule: Take 1 Step, Turn right, If obstacle take 4 steps left
Rule: Take 3 Steps, Turn right, If !right turn left, If detect dead end turn left, If next step !have two options, turn away

Encouraged by the variety of patterns that I was able to generate, I developed a program that mimicked what I was doing on paper. I simplified the rules to be less verbose and more explicit. The table below shows each command and its corresponding symbol.

Download Processing Sketch

Above, you can see the program in action. The rules for this system are as follows.

Ruleset 1: Move forward and turn right. [F+]
Ruleset 2: Jump two spaces. [JJ].

The program follows ruleset one until it encounters itself and follows ruleset two. Very quickly a pattern starts to develop and continues to grow until it reaches the end of the frame. By changing the two rules, a wide variety of patterns can be generated as shown in the gallery below.