Fractals03 of 113

Sierpinski triangle and polygons

Wacław Sierpiński, 1915

Pick a corner at random, move partway toward it, mark the spot, and repeat. Three corners and a halfway step put every dot on the triangle. With more corners and a shorter step the same game draws the Sierpinski polygons, and four corners with their four midpoints give the carpet.

zₙ₊₁ = zₙ + (1 − r)(vᵢ − zₙ), dim = log 3 / log 2 ≈ 1.585

On mathcurve.com as Triangle de Sierpinski

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Elsewhere

1

Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf

  1. 1231

    Cosmati pavement, Anagni Cathedral

    Cosmati workshop · Floor · Cattedrale di Santa Maria, Anagni

    Thirteenth-century marble floors where a triangle is filled with smaller triangles at least three levels deep. The resemblance to the Sierpinski triangle is a modern reading of the pattern; nothing records it as the masons’ intent.

    Not yet checkedSuggested by an AI model, 2026-10-08

    An AI reviewer had doubts, 2026-10-09: The holder's page says Cosmatesque work uses "elaborate inlays of small triangles and rectangles of colored stones and glass mosaics", so small triangles are attested. Nothing in the texts describes a triangle filled with smaller triangles three levels deep at Anagni, and there is no picture to show it, so the specific claim is unsupported.

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