non-conformal mapping   [→ Horn Torus & Physics home]
horn torus center
. . . or shown with the spread legs of Leonardo da Vinci's Vitruvian man :
Vitruvian man
←  mapping  /  sitemap  /  text  ⇓       ⇑  series of mappings
Vitruvian man mapping
series of mappings
series of Vitruvian man mappings onto horn of torus / still
( horn tori are good for more → jokes, e.g. this one)
Cat 'Schrödinger'

art project (1974 !!)
contemporary art (1974)
image title

similar project 1980
contemporary art (1980)
image title

similar project by Vyacheslav Puha - 45 years after the first above:
Puha's projections (2019)
Vyacheslav Puha also has generated very nice and meaningful animations concerning mapping (avi format):
download for your media player: world1world2world3 - © 2019 Вячеслав Пуха
content of videos:
world1: analytically generated conformal mapping from sphere to horn torus (left) and
geometrically generated mapping as stereographic projection (right)
world2: conformal mapping from sphere to horn torus and inverse, shown in one image
world3: conformal mappings between plane, sphere and horn torus (note mirroring on plane)
related mathematics

 In the stadium of grasping the priciple of dynamic horn tori all considerations about static mappings from two-, three- or any-dimensional space onto the horn torus surface - conformal or others - have no relevance for and no connection to the model, on the contrary, they rather might lead into a wrong direction. This digression only shows the geometric figure in a detail and should not be incorporated into the cognitive process (the considerations regarding horn torus mappings were launched by Vyacheslav Puha first and elaborated by Prof. Saburou Saitoh within a completely different project). Here on this site we primarily care about properties of dynamic horn tori!
 Later, long after one has found the appropriate image for complex numbers within the dynamic horn torus model, mappings conceivably can be used to establish correlations between pure mathemathics and human perception of 'reality'.


W. Däumler's font and image projections by artmetic graphic synthesizer, V. Puha's world projections by Mathcad