Sponge - named for its inventor Karl Menger and sometimes wrongly
called Sierpinski's Sponge – was the first three dimensional
fractal that mathematicians became aware of. In 1995 Dr Jeannine
Mosely, a software engineer, set out to build a Level 3 Menger Sponge
from business cards. After 9 years of effort, involving hundreds
of folders all over America, the Business Card Menger Sponge was
completed. The resulting object is comprised of 66,048 cards folded
into 8000 interlinked sub-cubes, with the entire surface paneled
to reveal the Level 1 and Level 2 fractal iterations.
Recipe for a Menger Sponge: Take a cube, divide it into 27 (3 x
3 x 3) smaller cubes of the same size - now remove the cube in the
center of each face plus the cube at the center of the whole. You
are left with a structure consisting of the eight small corner cubes
plus twelve small edge cubes holding them together. Now, imagine
repeating this process on each of these remaining 20 cubes. Repeat
again, and again, ad infinitum ... To make a Level 3 sponge, stop
after 3 iterations.
The Business Card Menger Sponge is being presented by the Institute
For Figuring and Machine Project in its first appearance to the
general public. On Sunday Sept 10, Dr Mosely will
present a lecture on the logical challenges of
decomposing this fractal form into manufacturable subunits and on
the structural considerations of building such a large object out
of business cards. The audience will be invited to make their own
business card cubes and to collaborate in making a Level 1 sponge.
coincides with OSME 4, the fourth international conference on Origami
in Science, Mathematics and Education, being held at Caltech.
Dr Jeannine Mosely is one of the pioneers in the emerging field
of computational origami, a branch of mathematics that explores
the formal properties and potentialities of folded paper. An expert
on the subfield of business card origami, she also conducts research
on curved crease origami, investigating the forms that can result
from non-linear foldings. Dr Moseley was trained as an electrical
engineer at MIT and works in the computer graphics industry writing
three-dimensional modeling software.
More information about the Business Card Menger Sponge and Dr Mosely’s
work on curved crease folding may be seen at the Institute For Figuring’s
This exhibition was assisted by grants from The Andy Warhol
Foundation for the Visual Arts and by the Annenberg Foundation.