(site-wide visits since 14/05/2005)
Toroidia
Adventures in Toroidal
Geometry.
(discuss
this)
I once met a guy on the Internet who told me that everything in the universe is made of circles of circles of circles.
A circle of circles is a toroid*; a circle of toroids is, for want of a better name, a supertoroid.
What you're looking at here is a spiral on the supersurface of a supertoroid.
This guy told me he knew by direct experience that this is the shape of Things.
One day I realised I knew how to animate it; the mathematics are straightforward enough.
There is still plenty to do with the maths, I think.
There is something strangely beautiful about toroidal convergence.
*This claim deserves some qualification. Specifically, a toroid is the shape made by a circle rotated about a point in the same plane as itself.
Return is the movement
of the Tao.
Yielding is the way of the Tao.
All things are born
of being.
Being is born of non-being.
Tao
Te Ching, ch. 40.
Enhanced, C++/OpenGL version this program now available!
Fully-rotatable view - click in main display; switch between spiral and symmetrical
versions; turn colours off...
Download Mac version (.dmg)
Download .cpp
Download .zip
(extract to a directory and move .dll files to your Windows/System directory)
(site-wide visits since
14/05/2005)