Fractals06 of 113

Barnsley fern

Michael Barnsley, 1988

Four affine maps, picked at random with weights of 1, 85, 7 and 7 percent, are enough to draw a fern. The 85 percent map builds the frond upward, the two 7 percent maps throw the lowest pair of leaflets, and the 1 percent map draws the stem. A breeze nudges the large map while you watch.

f₂(x, y) = (0.85x + 0.04y, −0.04x + 0.85y + 1.6)

On mathcurve.com as Fougère de Barnsley

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In the library

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  • Untitled (Fern Study), c. 1850, from the Hatton Fern Album, Unknown
    Untitled (Fern Study), c. 1850, from the Hatton Fern AlbumUnknownc. 1850The Art Institute of Chicago

    A real fern from a nineteenth-century album, to set beside the four-map one. Barnsley fitted his maps to the black spleenwort; this frond is not that species.

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

    An AI reviewer agreed, 2026-10-09: The note's facts hold up. The source says Barnsley modelled the shape on the black spleenwort, "He made it to resemble the black spleenwort, Asplenium adiantum-nigrum." The cyanotype is inscribed "Cistopteris Bulbifera", a different species, and the museum record dates it c. 1850, so it works as a real fern to set beside the four-map shape.

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