Random Walk

A close view of gold lines on purple paper. The lines move with random 90 degree rotations, but do not overlap. Some are short, others long enough to leave the frame of the image
Ongoing experimentation with random line generation
Print Date

Another interesting investigation into a fun technique for generating patterns — a random walk is the process of drawing a path using a set of rules and randomisation for distance and direction.

Early exploration

After a few attempts using truly randomised distances and rotations, I realised using something a little more structured was more to my taste.

The next few attempts used a set length for distance and multiples of 90 degrees for rotation and looked more organised. A problem I encountered was the tendency for the lines to layer up, which could result in over-saturated ink on the paper – I’ll eventually figure out how to de-duplicate stacked path segments.

This entire print is made using one continuous line per colour.

Purple and green lines on white paper. Each colour is slightly offset from each other so they overlap, but not completely. Each set of lines is mainly comprise of clusters of squares, with short straight lines connecting them. Some squares appear much darker, where they have been drawn over multiple times
This example has two different iterations printed together with an offset for some interesting effects

My next step was to come up with a simple system for drawing lines that don't intersect or overlap. It picks a point at random to start, checks for all empty adjacent spaces, then randomly picks one to move into. This is repeated until it ends up blocked in an area with nowhere to go. A new line is stared in a random spot and the process starts again. If the line starts with nowhere to go, I've decided to not print the single point.

In future I’d like to add functionality to either look further ahead or back-track, to avoid getting stuck as frequently.

The print order isn't the same as the generation order, so some lines look like they stop too soon during printing
Red and blue lines on white paper. Unlike the previous example, these lines are more organised and don’t intersect. Instead of one long line, it is made up of many shorter ones
Another example of the red and blue on white paper, but printed much more densely
Printing different iterations over each other for some colour blending
A single grid of lines, but this time lines are either teal, blue, green or purple. This allows each line to be recognised a little more easily
Using a range of colours to get a general overview of line length/distribution

Experimenting with clipping has also produced some interesting effects. In the following example, I've generated a full grid of lines, then removed any which intersect with the edge of a bounding circle.

A grid of gold and dark purple lines on purple paper. The dark purple lines give the illusion of a shadow to the gold lines. The overall shape of the grid is a circle, but some lines are missing, leaving it looking weathered and uneven
Two layers of printing – the first is a dark purple which gives a raised effect to the gold