Excerpt of a monohedral 11-gon tiling of a non-compact surface embedded in 𝑅³. (3 11-gons at every vertex)

The surface splits 𝑅³ in two, so that the space within the dodecagonal tunnels is on one side and the space in the hexagonal tunnels on the other.

The labeled dual edges of the tiling form a partial Cayley surface complex of the group:

G = ⟨ f₁, f₂, f₃, t₁, t₂, t₃, t₄ ∣ f₂², t₃², f₁², t₂², f₃², t₄³, t₁³, (t₁t₄)², f₁t₃t₄⁻¹, f₃t₁⁻¹t₂⁻¹, (f₁f₃)², f₂t₂t₃⁻¹⟩

(1/n) #tilingTuesday #math #3d #geometry #genuary

A program I wrote during Saturday's Creative Code Jam.

It's inspired by the Hilbert Sort algorithm, and asking myself the question: in what ways would I manually sort a fixed list of points, while generating a contour and avoiding intersections?

I thought that if I try many times I can discover algorithms in my head, then convert them into code.

The program is about 200 lines long and written in #Kotlin using the #OPENRNDR #CreativeCoding framework.

#geometry #math

This was an interesting problem to work on (back in 2017): A visualization of a path planner for 3D printing (FDM) a single layer/mesh structure of a multi-layer textile. Two setups of the same path strategy which optimized for longest continuous sub-paths and minimum rapids (distance without filament extrusion) between sub-paths. The planner supported six strategies in total, incl. optimizing for straight sub-paths and minimum amounts of "recent" crossings (to allow filament to cool down prior to crossing existing sub-paths)...

Submitted here for #genuary18: Unexpected path. Draw a route that changes direction based on one very simple rule.

#genuary2026 #PathPlanning #ThingUmbrella #Geometry #Mesh #3DP #Textile

Detail of a mosaic floor, Harris Museum, Preston, England

The Harris reopened in 2025 after a long redevelopment https://theharris.org.uk

#MosaicMonday #mosaic #geometry #tiling #tessellation #MathArt #design #pattern #photography

Made this for a friend who just started an #astrology business. I think it came out nicely.

#art #geometry