Here is an explanation for all of the traits in my on-chain generative series Perpendicular. The algorithm features multiple random walkers on a grid with collision avoidance. Once the random walk paths have been calculated, they are drawn in various styles.
Seed
A number determining the state of randomness. Generated from the transaction hash upon mint.
Size
The size of the grid cells. Ranges from Large to Tiny.
Palette
The colour palette. Some are from Field Trip and Block Party and some are new. Silhouette is the unique one where the lines are black and the background is colourful (below).
Number of Offsets
The number of offsets. Ranges from 1-30. There is a special case (below) where it is randomized per path but the rest of the time it is the same for all paths.
Color Style
Determines the arrangement of colours across the offsets of a path.
| Random: a random colour is chosen from the palette for each offset |  |
| Random Step: a random colour is chosen and then repeated until a set probability changes it |  |
| Solid: all the same colour |  |
| Solid Random Skip: all the same colour but there is a random chance of deletion |  |
| Solid Random Amount: all the same colour but there is a random number of offsets per path |  |
| Alternating: alternates between two colours |  |
| Gradient: interpolates between two colours |  |
| Sequential: the colours follow the order in which they are written in the palette. It is necessary for the Rainbow 7 palette to be displayed as a rainbow |  |
| Solid Dashed: one colour with dashed lines |  |
Straightness Probability
Determines the jaggedness of the random walkers. Left/Right probability are set to 2 and straightness probability ranges from 0 to 15. If it is zero, the walkers are forced to turn every step (below).
Corner Loop Probability
Determines the likelihood of corner loops appearing. 0 means none will be present. Corner loops break the no-visiting-where-it’s-been-before rule for walkers because they have to cross over themselves.
Corner Style
Determines whether corners are straight or round.
Thickness
The width of each individual offset line. Ranges from 0.5 to 1.
Spread
How much of the width of the grid cell the offsets are multiplied by. Ranges from 0.75 to 1. A thickness of 1 and a spread of 1 are necessary to get lines with no gaps between paths (below).
Distortion
Applies visual distortion to the image of the random walker grid. Only happens when corner style is straight.
Border
Creates a border around the entire random walker grid. Only happens when distortion is 0.
Square Style
Style of any squares leftover after all random walkers have been placed. The large size grid usually only has up to 4 left over spaces, in which case they aren’t drawn.
| Small Shapes: little squares, all the same colour |  |
| Squares: one size of squares, all the same colour |  |
| Random Squares: one size of squares, random colours |  |
| Multi-scale Squares: random size of squares, all the same colour |  |
| Grid: outlined squares |  |
| Connected Grid: outlined squares with adjacent ones connected by a dash |  |
| Connectors: only the connecting dash |  |
| Random Connectors: only the connecting dash, randomly coloured |  |
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