Saturday, November 1, 2008

Impossible fractals

 A spiral tri-bar and hexagonally bound isometric spirals

An impossible fern (balanced 30° Pythagorean tree).

An impossible mushroom (45° Pythagorean tree).

45° Pythagorean tree, balanced 30° Pythagorean tree and extended tri-bar

Reutersvärd's "Meander" and a Hilbert meander

An impossible multibar Peano-Gosper curve.

Ernst's "Nest of impossible cubes" and two variations.

Subcube designs and Buch's "Cube in blue".

An impossible multibar cube and the Menger sponge after one and three iterations

Four-bar designs (with sharp and truncated generators) applied to the square Sierpinski curve

The Devil's gatling gun (two levels), timber offcuts (two levels) and comb (three levels).

The Devil's fork and the Cantor set.

Impossible gaskets are more troublesome

An alternative snowflake design that emphasizes the perceptual effect (with generator shown).

Two iterations of an impossible snowflake (with acute and obtuse generators shown).

The tri-bar, the Koch snowflake and the Sierpinski gasket.

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