ReciprocArt is a project to explore the mesmerizing diversity of the Fourier space. Every image is the result of a Fourier transformation (FT) of a custom-made pattern: you can flip between them by clicking on each image.
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 spectra exist in what is known as Fourier space or ‘reciprocal space’, where features are linked to order and disorder in the distribution of pixel intensities in 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 their corresponding pattern. The size of this extension is included in the caption (e.g., ‘crystal size’).
All my creations are protected by an ‘all rights reserved’ copyright. If you want to own one, you can reach out to arrange a unique version for you. I never make any pattern twice, so your image will be absolutely unique.
1. Aperiodic "Ein-Stein" monotile and its Fourier transform (crystal size: 150 tiles radius)Tiling creation credits: cs.uwaterloo.ca/~csk/hat/app.html2. Moroccan mosaic and its Fourier transform (crystal size: 20 unit cells radius)3. "Shells and Starfish" by M. C. Escher and its Fourier transform (crystal size: 40 unit cells radius)4. Penrose tiling #1 and its Fourier transform (crystal size: 500 tiles radius)Tiling creation credits: https://aatishb.com/patterncollider5. Alhambra tiling and its Fourier transform (crystal size: 50 unit cells radius)6. Ocellated lizard skin pattern produced by MC simulations and its Fourier transform (crystal size: 100 unit cell radius; inspired by "Lizard Skin Patterns and the Ising Model" by S. Zakany et al.)7. Fractal 太極圖 (tàijítú) mosaic and its Fourier transform (crystal size: 80 unit cells radius)8. Handmade truchet tiling (10 type of tiles) and its Fourier transform (crystal size: 40 tiles radius)9. Handmade mosaic and its Fourier transform (crystal size: 12 tiles radius)10. Penrose tiling #2 and its Fourier transform (crystal size: 500 tiles radius)Tiling creation credits: https://aatishb.com/patterncollider11. Polygons of Porygons (ポリゴン) and their Fourier transform (crystal size: 14 polygons radius)12. Moiré pattern #1 and its Fourier transform (crystal size: 130 unit cells radius, tilt angle 9°)13. Sierpiński triangle and its Fourier transform (fractal dimension: 3^7 triangles)14. Crossed 'golden ratio' radial curves and their Fourier transform (total number of curves: 128)15. Kaleidoscope of a handmade fruit tart and its Fourier transform (crystal size: 30 fruit tarts)16. Handmade Hitomezashi (一目刺し) pattern and its Fourier transform (crystal size: 244 segments ratio)17. Disordered chocolate squares #1 and their Fourier transform (crystal size: 690 chocolate squares radius)18. A quasi-snowflake and its Fourier transform (fractal dimension: 6x5^6 pentagons)19. Hilbert curve and its Fourier transform (curve extension: 10 iterations)Curve creation credits: https://onlinemathtools.com/generate-hilbert-curve20. Dragon curve fractal and its Fourier transform (curve extension: 19 iterations)Curve creation credits: https://dragon.best/curve/21. Composition of circles and its Fourier transform (number of circles: 800)22. Aperiodic tiling from periodic sequence of tiles, and its Fourier transform (Crystal size: 320 tiles radius, number of tiles in the repeating sequence: 3)23. A Totoro (トトロ) crystal and its Fourier transform (crystal size: 160 Totoros radius) Created on World Mental Health Day to remind us to be kind especially to those who act mean or weird due to their hidden struggles. Be soft, be Totoro.24. A pattern of Laue patterns, and its Fourier transform (Crystal size: 8 unit cells radius; ZIF-90 [111])25. Menger sponge fractal and its Fourier transform (Fractal dimension: 8^8 squares)26. Aztec diamond and its Fourier transform (number of iterations: 800)Pattern creation credits: https://sherpal.github.io/aztec-diamond-generator27. Dendritic structure (Kobayashi model) and its Fourier transform.Pattern creation credits: https://github.com/GollyGang/ready28. Periodic framework of pentagons and its Fourier transform (crystal size: 12 unit cells radius)29. Vicsek fractal and its Fourier transform (Fractal dimension: 5^5 crosses)30. Tagliatelle alla Truchet and their Fourier transform (crystal size: 420 tiles radius; 3 types of tile)31. Aperiodic Pacman labyrinth and its Fourier transform (crystal size: 85 tiles radius; 4 types of tile)32. E-toothpick sequence and its Fourier transform (number of iterations: 200)Pattern creation credits: https://oeis.org/A139250/a139250.anim.html33. Hexagonal Hitomezashi (一目刺し) pattern and its Fourier transform (Crystal size: 250 segments ratio)34. "Spectre" aperiodic chiral monotile and its Fourier transform (crystal size: 75 tiles radius)Tiling creation credits: https://cs.uwaterloo.ca/~csk/spectre/app.html35. A Quick Response code and its Fourier transformQR code creation: https://github.com/lincolnloop/python-qrcode Source text: Abstract of "Polynomial Codes Over Certain Finite Fields" by I. S. Reed and G. Solomon36. Fibonacci word curve and its Fourier transform (number of words: 26)Curve creation credits: https://rosettacode.org/wiki/Fibonacci_word/fractal#Python37.38. A spider web and its Fourier transform39. A jigsaw puzzle and its Fourier transform (Puzzle size: 25600 pieces) Picture for the puzzle: "Europe divided into its kingdoms, etc." by John Spilsbury, 176640. 'Shuriken' hitomezashi (手裏剣 一目刺し) pattern and its Fourier transform (Crystal size: 200 segments radius)41. An H6X9H curve (N=689; D=628) and its Fourier transform.Curve creation credits: www.tistis.nl/H6X9H/42. Intersection of two hexagonal patterns of circles (relative tilt angle = 90°) and its Fourier transform.43. Multivariate distribution of colours in a molecular structure and its Fourier transform (4 variants of correlation parameters, one for each quadrant of the image).44. Close packing of 6-sided dice and their Fourier transform (crystal size: 50 dice radius)45. Square version of the "Healing grid" optical illusion by Ryota Kanai, and its Fourier transform.46. Domain boundaries and strain emerging from simulated phyllotaxy, and its Fourier transform. Matthew Pennybacker and Alan C. Newell. (2013), Phys. Rev. Lett. 110, 248104;Pattern creation credits: https://github.com/GollyGang/ready48. Composition of pentagons according to a custom rule, and its Fourier transform. Number of pentagons: 3x(5^4)49. A 'kissing circles' fractal and its Fourier transform (Number of circles: 1+7^6)50. Disordered tiling inspired by "Composition in Red, Blue, and Yellow" by Dutch artist Piet Mondrian, and its Fourier transform (number of rectangles for the FT: 10^4) The tiling is created by generative coding in Processing. The source script is an adptation of the one available at github.com/erdavids/Mondrian-Tiles/blob/master/Mondrian_Tiles.pyde51. A barcode (code type 128) and its Fourier transform. The information contained is a sentence by Norman Joseph Woodland to describe the 'Eureka' moment that led him to the concept of barcodes: "For whatever reason I pulled my hand toward me and I had four lines".Barcode creation credits: generator.opticon.com52. A 'honey sponge' fractal and its Fourier transform (Number of hexagons: 6^7)53. Composition of triangles and squares with features reminiscent of fractals, and its Fourier transform.54.55. A handmade "missing stars" optical illusion and its Fourier transform. Number of 12-pointed stars used for the curve: 17.56. Moiré intersection of two square tilings of squares and its Fourier transform. Relative tilt angle: 43°.57. Hyperbolic tiling of triangles and its Fourier transform. Curve generation parameters: 7 polygons per vertex, layer depth 11.https://pypi.org/project/hypertiling/58. Greys whirlpool (handmade optical illusion) and its Fourier transform. The size of each section is modified by an inward exponential decrease with factor 0.75.