There is an important difference between the pictorial representation of of the set (body) of complex numbers by a static horn
torus and my model. First is a mapping* from the complex plane via Riemann sphere to the horn torus within the three-dimensional space,
whereas 'my' horn tori are dynamic: they execute rotations around the main symmetry axis and revolutions of the torus bulge
around itself. They change their size and they are many, as many as 'particles' in our universe, all nested into one another, all
intertwining at one ('spatial') point. They are not embedded in any three- or more-dimensional space, but every horn torus
'entity' embodies one coordinate of an infinite-dimensional space. The static horn torus is a rather simple figure with little
properties. Its incredible complexity and creative capability only arises when the dynamic is added, as described and illustrated on
these webpages. ( visualisations e.g. explanation , trajectories , resonances )Mathematically associable English texts e.g. can be found on pages starting here, but to treat the matter really mathematically, one first of all has to conceive the principle, what in my view only can be transported as colloquial speech. I know that is not the mathematician's way to cognition, but I treat it as a more philosophical and fundamental physical topic, though: 'my' horn tori represent complex numbers too - only differently. Their dynamic shows the capability of complex numbers 'quasi to calculate with themselves and mutually with each other' - as creators of our
world.→ front page / sitemap / previous page *) example for a mapping that preserves right angles between coordinates: |

upper and lower *edge* of the plane both correspond to the center *point* of the horn torus (but note:
it is *not* the complex plane!)

horn torus latitudes maintain distance, while longitudes converge in vicinity of horn torus center - for full conformal mapping the latitude scale has to converge with same (sinus) rate as for
longitudes (on Riemann sphere: arctan),
otherwise we obtain deformations of structures and patterns as in this image , part of horn torus art , or - nicely seen - with an animated hexagonal pattern , but note: the structure-producing dynamic
horn torus is non-conformal! (why should it be conformal?) |