Make a geometric pattern with code
Build a tiled geometric system by defining one cell, checking its edges, and introducing variation that respects the connections between neighboring tiles.
The pattern begins at its borders
A repeat pattern succeeds at the edges of its smallest unit. Start with a tile whose marks enter and leave at known points. When those contact points agree across neighboring cells, you can rotate or swap the tile while preserving larger paths that seem to grow beyond it.
Repeat a curve through rotated cells
Draw a square tile with a curve joining two edge midpoints. Put the drawing in a function that accepts an origin and rotation. Translate to the cell center before rotating. Repeat across a small grid and use temporary cell outlines to expose mismatched connections.
Make cell size explicit in the working notes before building the full piece. Keep the ordinary state beside the most extreme intended state. The useful boundary is where the relationship remains understandable, rather than where the tool stops allowing a larger value. Check both ends before filling the middle. A useful acceptance check is whether adjacent curve endpoints join without visible jumps. Judge that at the intended viewing size or working distance, where tiny construction mistakes and exaggerated effects can have very different consequences.
Check endpoints and rotation centers
If curves meet with a step, compare their endpoint coordinates before adjusting their curvature. If rotated tiles slide out of place, inspect the rotation origin. Increasing the grid size hides these mistakes visually while making them harder to locate.
When the result becomes confusing, return cell size to its recorded starting point. Temporarily show construction points and intermediate values. Reduce repeated elements to a handful and pause anything that changes over time.
Compare three tile arrangements
Create three arrangements using the same tile: all identical, alternating rotations, and selected random rotations. Compare how much structure emerges at scales larger than one cell. Keep a small tiled proof beside the full image.
Make three comparison versions using 24, 48, and 96 pixels. Choose one visible feature to compare before starting. Inspect it across the entire set rather than letting the most dramatic result dictate the criterion afterward. Keep both a preferred version and a useful failed version, with a short note describing the difference between their behavior.
Test a two-by-two proof
Before filling a large canvas, place four tiles in a two-by-two block and inspect the shared central junction. This small proof exposes endpoint and rotation errors on both axes. Draw a tiny marker at every edge midpoint while testing. If the marks meet but the curves seem discontinuous, compare their arrival directions; connected positions can still produce a visible kink when the neighboring tangents disagree. Compare the junction in all four rotations before declaring the tile interchangeable.
A tiled garden path
Build a looping garden path from quarter-circle arcs in square cells. Use only two permitted orientations and leave one row unvaried as an anchor. The pattern should suggest many routes while still giving the eye somewhere stable to enter.
References & further reading
Examples and exercises in this guide are original teaching scenarios.
