OneTaskBy Tim King · Updated
Islamic Geometric Pattern Generator
Seamless Star and Polygon Tiles, Free PNG
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How the Islamic Geometric Pattern Generator works
This Islamic geometric pattern generator draws star and polygon tilings. The star-and-polygon patterns of Islamic architecture are built from a tiling of regular polygons and one rule for the lines that cross each polygon. Choose a grid of octagons and squares, plain squares or hexagons, set the contact angle that turns the lines into eight-, four- or six-pointed stars, pick lines or interlaced bands, and save a seamless PNG tile. Nothing leaves your browser.
Islamic geometric pattern generator: how the pattern is built
Every design here follows the polygons-in-contact method, the construction that historians credit to the medieval craftsmen and that Ernest Hankin described in 1925. Start with a tiling of regular polygons. At the midpoint of every polygon edge, two lines leave at the same angle to the edge, one each way, and each line runs until it meets the line from the next edge along. Because neighbouring polygons share an edge and use the same angle, the lines join across the edge and the polygon boundaries vanish, leaving stars where the polygons were and connecting shapes between them. The grid never appears in the finished tile; it is the scaffold the pattern hangs from.
Grids and their stars
Octagons and squares is the classic combination behind most eight-pointed star patterns, with an octagon in each cell and a small square at every corner; at a 45° contact angle the lines form the familiar khatam star and cross motif. Squares alone gives a four-fold lattice that reads as woven strapwork, and Hexagons gives six-pointed stars and the honeycomb strapwork of North African and Andalusian zellige. Cells across sets how many polygons fit in a tile, so a low count gives large stars and a high count a fine, dense lattice.
Contact angle
The angle between each line and its edge is the single control that changes the character of a pattern. Low angles, around 20 to 30 degrees, produce thin stars with long, sharp points and large open shapes between them; 45 degrees gives the balanced star most people picture; and angles above 60 produce fat, rounded stars that almost touch. The stat under the canvas reports the angle and the fold of symmetry the grid produces.
Lines and bands
Lines draws every segment as a single stroke in the palette's ink colour. Bands draws each segment as a wide band of ink with a narrower stroke of the background colour down the middle, which gives the look of two parallel lines with a channel between them, the strapwork style used in carved wood and stone. Line weight is a percentage of the cell, so it scales with the grid and with the export size.
Seamless tiles and saving
The tile holds a whole number of cells in each direction and the polygons that cross the tile edge are drawn again on the opposite side, so the lines continue across the boundary and the tile repeats without a seam. Export a square tile at 256, 512, 1024 or 2048 pixels or a tiled wallpaper at 1920 × 1080 or 3840 × 2160. Files are PNG, drawn on a canvas on your machine and saved straight from the browser.
FAQ
Can this make ten-fold or twelve-fold patterns?
Not in this version. Ten-fold designs need a girih tiling of pentagons and decagons that cannot repeat on a square tile, and twelve-fold needs a hexagon-and-dodecagon grid. The three grids here cover the four-, six- and eight-fold families, which account for most tiled star patterns found on walls and floors.
Why do the shapes between the stars change with the angle?
The lines from adjacent edges meet at a point whose position depends on the angle, so the same grid gives a different set of polygons around each star. Sweep the angle slowly and the pattern morphs continuously, which is the quickest way to find a design you like.
Is the pattern culturally accurate?
It uses the same geometric construction as historical patterns, and the octagon grid at 45° reproduces a design found across the Islamic world. Colours and proportions are chosen for screen use rather than copied from any one building, so treat it as a starting point rather than a reproduction.
Which settings give a classic Alhambra look?
Choose Hexagons, 6 cells across, an angle of about 60, Bands, and the Ivory and indigo or Turquoise tile palette. For a Cairo or Damascus woodwork feel, use Octagons and squares at 45° with Bands and the Sandstone palette.
See also: all Generative Art tools, Images, Audio, Video & Screen, PDF, SVG, Simulations & Screensavers, Chart Makers, 3D Model Viewers, Drawing Pads, Mockups & 3D Making, Diagram Makers, 3D Science, Tracker Music.
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