Cameron Browne. Impossible fractals

This paper demonstrates ways in which fractal techniques may be applied to impossible object designs, with mixed success. While some designs resist fractal development, others prove amenable and can even yield pleasant surprises, such as the emergence of the second type of illusion in the Hilbert meander.

The combination of the extended tri-bar with the Pythagorean tree demonstrates that the perceptual effect can be successfully maintained at continuously decreasing scales in the one design. Tree balancing provides a way to render such designs efficiently.

Practical applications for the techniques discussed above might include the production of large format art works that display the perceptual effect to many more levels of recursion that the figures in this paper allow; the effect could then be seen at multiple levels, depending on the distance at which the picture is observed. Future work might include the creation of such large format pictures that include different types illusions at each level of scale.