ReciprocArt ◦ Tilings
ReciprocArt is a project to explore the mesmerizing diversity of the Fourier space. Every image on the right-hand side is the result of a Fourier transformation (FT) of a custom-made pattern, shown to its left.
FT is a mathematical processing method that, when applied to an image, produces a new one containing a spectrum of all pixel-pixel frequencies present in the starting image. Such spectrum exists in what is known as Fourier space or 'reciprocal space', where features are linked to order and disorder in the distribution of pixel intensities within the original image.
Every pattern is original when not stated otherwise. To obtain sufficient inter-pixel correlations for avoiding artefacts in reciprocal space, many of the following FT images are created from an extension of its corresponding pattern. The size of this extension is included in the caption (e.g., "crystal size").
Aperiodic "Ein-Stein" monotile and its Fourier transform (crystal size: 150 tiles radius)
Tiling creation credits: https://cs.uwaterloo.ca/~csk/hat/app.html
Moroccan mosaic and its Fourier transform (crystal size: 20 unit cells radius)
"Shells and Starfish" by M. C. Escher and its Fourier transform (crystal size: 40 unit cells radius)
Penrose tiling #1 and its Fourier transform (crystal size: 500 tiles radius)
Tiling creation credits: https://aatishb.com/patterncollider
Alhambra tiling and its Fourier transform (crystal size: 50 unit cells radius)
Handmade truchet tiling (10 type of tiles) and its Fourier transform (crystal size: 40 tiles radius)
Handmade mosaic and its Fourier transform (crystal size: 12 tiles radius)
Penrose tiling #2 and its Fourier transform (crystal size: 500 tiles radius)
Tiling creation credits: https://aatishb.com/patterncollider
Moiré pattern #1 and its Fourier transform (crystal size: 130 unit cells radius, tilt angle 9°)
Aperiodic tiling from periodic sequence of tiles, and its Fourier transform
(Crystal size: 320 tiles radius, number of tiles in the repeating sequence: 3)
Periodic framework of pentagons and its Fourier transform (crystal size: 12 unit cells radius)
"Spectre" aperiodic chiral monotile and its Fourier transform (crystal size: 75 tiles radius)
Tiling creation credits: https://cs.uwaterloo.ca/~csk/spectre/app.html
Tiling creation credits: https://cs.uwaterloo.ca/~csk/spectre/app.html
Intersection of two hexagonal patterns of circles (relative tilt angle = 90°) and its Fourier transform.
Multivariate distribution of colours in a molecular structure and its Fourier transform
(4 variants of correlation parameters, one for each quadrant of the image).
Close packing of 6-sided dice and their Fourier transform (crystal size: 50 dice radius)
