horn torus entity
x = r·(1 − cosφ)·cos(φ2/2π)
y = r·(1 − cosφ) · sin(φ2/2π)
z = r · sinφ
r = r1·φ / 2π for r > r1
r = r1·2π / φ for r < r1
φ = 2π when r = r1 *)
φ < 2π doesn't occur !
φ is the poloidal horn
torus angle, r in the graphic above is not to scale,
increments of the single steps
rough, depicted is the section
between 4 revolutions per 1 rotation
and 100 rotations per 1 revolution
(for explanation click image)
*) r1 signifies the
standard dynamic horn torus, the 'μ-sterious'
'infinite outer world', consisting of electrons and photons, and the 'small inner world' of
Important note 1 in this context: the widely unknown infinitesimal infinity has the
same cardinality as our known large universe (i.e. nuclei comprise whole universes).
It's worth to think about that!
Note 2, equally imperative: horn torus depictions are allegoric only, their purpose is
to symbolise mathematical particle properties - they don't occur as objects in
our familiar 3-dimensional space.
Dynamic variation of poloidal revolution and toroidal rotation, combined with
alteration of size, can be expressed smartly by complex and hypercomplex numbers
(quaternions, octonions, ...) - but
to describe the whole dynamics as abstract physical processes, including the
interaction of intertwined nested horn tori, seems to be a task, which is
not manageable by conventional
so, in this regard, the author is not ready yet :-(