Saturday, January 17, 2015

Da Vinci's Tree of Life - Brain

'Tree of Life' with knots by Leonardo Da Vinci in the Sala delle Asse in Milan.





Similar to arabesque art: "The very term arabesque is a rather diffuse one, sometimes used broadly to denote almost any style of geometric ornamentation prevalent in Islamic nations, but here I will take it as referring more specifically to stylised vegetal decoration ‘in which plants and leaves grow according to the laws of geometry rather than nature,’ forming ‘interlaced straps, zizags, spirals, scrolls and knots’ which tend to fall into complicated polygonal shapes, in turn forming separate frames for other patterns inside them. Use of this type of decoration, which apparently originated in 10th-Century Baghdad, became widespread throughout the Islamic world in the following centuries." - www.spamula.net


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Related to Knot theory: “In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone.” - http://en.wikipedia.org/wiki/Knot_theory


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But probably an homage to the astonishing Albrecht Dürer, a German painter, mathematician, and theorist who was a friend of Leonardo.


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Though it might also have been a subliminal expression of the knots, wires and connections in his brain ; p




Tuesday, December 16, 2014

Akasha


This dancer comes close to how it feels when I'm imaging the motion of particles in my mind : )

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On a funky sided note 'Akasha Tattva' is the 0val particle that is the Aether:

"Akasha (or Akash, Ākāśa, आकाश) is the Sanskrit word meaning "aether" in both its elemental and metaphysical senses.

Akasha is space in the Jain conception of the cosmos. It falls into the Ajiva category, divided into two parts: Loakasa (the part occupied by the material world) and Aloakasa (the space beyond it which is absolutely void and empty). In Loakasa the universe forms only a part. Akasha is that which gives space and makes room for the existence of all extended substances." http://en.wikipedia.org/wiki/Akasha


Akasha - Spirit - black or indigo vesica piscis or egg.


The mathematical ratio of the height of the vesica piscis to the width across its center is the square root of 3

Monday, December 15, 2014

Storyboard


(J. Lampel & F. Steinmetz)


(Shantamo)

Rough storyboard for the movie:

Animated gif version:

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Hello World,

I'm trying to get a visualisation going but I'm running slowly out of steam. So if you would be interested in joining up to this project or want to sponsor to hire an A-Team like these guys ...

http://www.aixsponza.com/projects/terra-mater/



... than don't hesitate to email me at:


Thanks!

Tuesday, November 25, 2014

Sunday, November 16, 2014

Back Bone & Grid


Saturday, November 8, 2014

Processing


Particle Pair Creation

Torus Formation (Snake & Apple)


Medium

Monday, September 15, 2014

Harmonograph / Elementary Rhythmic Patterns

A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image ...

(source: Wiki + BirdandBee)

The most elementary patterns are:
Torus (Open phase - unison 1:1) 
Fig. 8 (Open phase - octave 2:1) 
Trefoil-knot (Counter current - octave 2:1) 

(Source: Wooden book Sacred Number)

Sunday, August 24, 2014

Connected Funnels


1. There is a motor that keeps the big wheel spinning.
2. There is a connection between small and big : flow / transmission.
3. The big wheel acts like a Flywheel with lots of potential energy.

-- Falcao Soliton / U-Tube --

4. Now for the transmission between the big and the small wheel, like a bike, you need a chain/flow and they have to be able to rotate at dependently. This you get when you have a diagonal flow which is the case for the vortices in the water, when there’s a sinkhole or a connection.
5. So there are two different wheels with two different velocities.
6. To get this you need a structure (which is generated by the movement with the dinner plate).
7. This all brings us to the Torus which is a large rotating Flywheel, and a small inner wheel string-shape : Funnel.
8. Same thing for the fig. 8
9. The string in between also causes for dissipation so everything is in balance and can keep on going. Suction on top with the Open funnels, Dissipation along the wire.
10. The different rotational direction of the 2 U-turn vortices keeps the connection flow in balance, like the chain-link of a bike but twisted.
11. There’s an overal equilibrium state thanks to a 3 Dimensional structure.

Friday, August 15, 2014

Extra Dimensions (V=1)


  • 1D: you can keep a steady line; with a velocity in the x=1
  • 2D: you can keep a stationary formations: square, circle … or a wavy path; the velocity becomes a combination of xy
  • 3D: to move those rotating 2D formations forward you need a 3th dimension (xy-z). Because if you move a rotating formation forward in 2D, every particle starts to have a different velocity, only by adding an extra dimension is it possible to move them together forward in a particular direction, and keep their formation rotation going.
  • 4D: to move those round or forward moving formations, one needs again an extra dimension; xyza

Nutcracker

Saturday, August 2, 2014

Closed Hilbert Curve

After finding a topic on Continuous Fractal Space-Filling (Hilbert) Curves ...


... in a math-book in the library this week ...


... I started looking for them on the internet and came across a neat tool on the Wolfram-site:

(CDF player: http://www.wolfram.com/cdf-player/ - 200 Mb or so)

But because the curve was open, I asked the developer Dr. Michael Trott if he could ad a closing option, like the picture in the book … and hey! he send me this adjusted cdf-file/code where the loop is closed ... et voilà there was the Fig. 8 knot, check it out:
http://800million.org/InterpolatingTheHilbertCurveWithABSplineClosed.cdf

Friday, July 11, 2014

Ovals & Trefoil Knot


Proportions