Hello Vortex People,
This is some serious stuff to me as a hobby. I call it a hobby so
people won't think I'm too serious.
But seriously, a certain group of knots on the same donut afford a
golden opportunity to get organized and orderly on the torus surface <--
with a magnetic vector wave continually revolving at velocity by
frequency per scale.
A certain group of entangled knots affords what I always thought was
going to be easy to do. Well, just winding a helix around a donut
multiple times, entangling with the earlier windings, and connecting
where it started as a 'smooth' torus knot, gets the
surface-velocity-timing of the vector rotation all mixed up. Don't despair!
---
Brought to you by shear boredom during panedemania...
There is a way to wind a group of smooth torus knots on a torus surface,
in such a way that the torus knots are energized in step-phased
electrical current, smoothly and continuously over the surface.
The trick is not a 'way to do it', but which knots to smoothly entangle
when separated by 120 degrees each around the donut <-- and this trick
appears and disappears by the number of entangled phases. This focus
will be only about 3-phase.
The answer of which knot to use is --> 13:8 <-- The p:q knot ratio turns
around the torus axis (p) and helical loops through the torus hole (q).
Or, that's my personal choice.
The 3:2 knot, the 13:8, and the 55:34 are the first three knots which
also share the quality of 1) q = even number, and 2) p and q are
adjacent numbers in the Fibonacci sequence.
---
Hot or Knot?
What's your vote as a sensible knot for prototype studies toward
revolving a magnetic vector tangentially and continuously around the
surface of a golden donut (by torus profile) at a golden slope through
the torus plane, and a golden slope from the axis through the torus hole?
---
Why q = even numbers?
Because, for even q-s, the electrical connection points for bifilar
conduction are diametrically opposite each other on the outer
circumference of the donut.
So? Because then, electrical connection is performed away from the
torus center hole, and all connections for 3-phase group of knots on a
donut are done on a six-point layout, as a hexagon. A magnetic
self-resonance on the knot group (at a few megaHz of ring-amp tail-chase
current-reversals for maximized delta-B) will have minimal magnetic
interference leading away from the magnetic surface of the copper array,
a copper wound donut. There's nothing in the center hole of the donut
but the hole (and perhaps some target for study, like a very thin film
of nano-fibers for hosting plasmon resonance as a emergent-topology
enticement for over-driven states.
---
Why Fibonacci neighbors?
Beside being an approximation of the golden ratio, the Fibonacci knot
ratios produce this curious de-tangling of entangled knot helices.
Each knot self-entangles its own windings, and when two are entangled on
the same donut (none touch, the loops are between the first knot's
loops) there is yet an entangled pattern on the torus surface.
But wait!
When a third Fibonacci knot is wound between two other knots on a donut,
all smooth, even, non-touching, and symmetric, then two geometric
structures appear in the order and current flow along the surface of the
knot:
1) The left-handed and the right-handed helices (the bifilar halves)
are grouped contiguously, symmetrically, and in sequence; and
2) The phase order is natural as phaseA, phaseB, phaseC, phaseA,
phaseB, phaseC.... across the entire surface. Which is what I
thought would happen in the beginning when one just wound a bunch of
wire on a donut. Nu uh. But now you know.
---
How can this be?
Without knowing the proper terminology, suffice to say it is about
dissonance near an integer. The golden ratio creates an even
distribution on a plane in seed-heads of plants, or phylotaxy of leaves
on a stem, but entangling golden entanglements on a golden donut creates
a sorted progression of polarity and phase. I be happy.
---
What this is?
This is about reverse-engineering attempts to design 'it' to comply with
what's not known to not work. No government funds were used, or animals
harmed (not counting my neurons).
---
What size this is?
It's about a foot across the outer diameter of the copper wound donut.
The hole of the donut is about a quarter of an inch" (6 mm). There will
be 39 helical twists in 3-phases, with about 50 foot total copper
conductor (likely flat conductor for the close spacing in the hole.
---
What power's this geometric magic knot array?
Something like two D.C. arc-welders in series for a power equivalence,
as an over-engineered prototype build. As a test-device, this leaves
room for adjustment.
Whirls,
Don
