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In
MATLAB . . . . . . .
Möbius Animation
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Copyright Notice:
The animation and all images within are under copyright by Cye H.
Waldman
and may not be copied, electronically or otherise, without his express
permission.
Cye H.
Waldman, cye@att.net
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You are looking
at an optical illusion. The cross-section is an astroid.
The
animation is a tromp l'oeil in that the object is rotating about the
vertical axis. However, there is a stroboscopic effect due to the
fact
that the rotation rate matches the radial ribs, which then appear to
stand still. The net effect is that the object seems to rotate
about
the circular ring, much like a ring vortex.
Three-dimensional Möbius forms, or "Mobioids" are created from toroids
by a radial cut, one or more twists, and reattachment. This
is remarkably similar to a Penrose triangle.
Interestingly, for
a toroid with five surfaces, any number of twists
where n is not disivible by 5
will produce a single surface. In
addition, the generating toroid need not be circular.
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Look for a
cross-section:
Two surfaces
and two cusps
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Look for a cross-section:
An Astroid with four cusps
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Curve
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