Fractal foundation of Fluid Mechanics

[jehovajah]

<a href="http://www.youtube.com/v/llqBmy&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/llqBmy&rel=1&fs=1&hd=1</a>

http://m.youtube.com/watch?v=llqBmy_Ax50

Turbulence has an almost inverse square law, again suggestive of rotational dynamics affected by trichoidal behaviours. Not easy to see unless you are looking for it as a fractal spaciometry.

The Stoikeia, an introductory discourse on the Pythagorean philosophy at an undergraduate level guides the student into thought patterns that make these dynamic relationships apprehensible. The relationships themselves are scale invariant, and so fractal in that sense, but definitely fractal in the sense of approximation to a smooth continuity. Discreetness of form is not discontinuity perse but it is akin to discontinuity of perception. The isolation of the invariant forms , distinguished only by scale and orientation is akin to discretisation of an otherwise imperceptibly continuous dynamic.

And it is form that we perceive, however fleetingly , however dynamic. To denote this as a fractal perception, a rough and ready approximation of a continuous experience of extensivity and intensivity , curvilineal in generality is one of the intellectual tour de force of modern natural philosophy .

While Cantor and his set theoretical infinities are a misleading attempt to describe continuous dynamics , nevertheless the attempt to capture these notions of perceptible reality are pertinent even if esoteric.

We can not count on mathematics to depict this if Mathmythics is allowed to obscure the inquisitive intellect of Natural Philosophers.

How we may apply ourselves to investigating and depicting these dynamics is given in the Stoikeia, the Conics and the Spherae of Pythagorean scholars down through the ages, of whom the most Noteable is Newton, and of course Benoit Mandelbrot.
<a href="http://www.youtube.com/v/TnkgG0wSVng&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/TnkgG0wSVng&rel=1&fs=1&hd=1</a>
http://m.youtube.com/watch?v=TnkgG0wSVng

<a href="http://www.youtube.com/v/jiMyzYf&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/jiMyzYf&rel=1&fs=1&hd=1</a>

http://m.youtube.com/watch?v=jiMyzYf_COA

[jehovajah]

<a href="http://www.youtube.com/v/SKoaFgvsogs&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/SKoaFgvsogs&rel=1&fs=1&hd=1</a>

http://m.youtube.com/watch?v=SKoaFgvsogs
An inverse law that indicates rather than defines rough behaviours. But what ubbdelies these behaviours is trochoidal dynamic.
Why?
Frequency distributions are not smooth as frequency changes relative to each other. There are dynamic ranges where smooth changes do occur suddenly to be interrupted by wild incoherent motions.

Many fractal sculptures show this "uninteresting" result which hitherto I had not understood the significance of .

[jehovajah]

<a href="http://www.youtube.com/v/NjHUi1BvXRg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/NjHUi1BvXRg&rel=1&fs=1&hd=1</a>

http://m.youtube.com/watch?v=NjHUi1BvXRg

I have said it many times : the simple fractal generator is a tool fr studing dynamic and physical, chemical systems, in particular as I have extensively meditated upon in the magnetic universe forum. The phenomena of Magnetic behaviour and electrodynamic behaviour, sound , heat and light.  Google jehovajah a sound basis of rotational dynamics

[LMarkoya]

THank you for the links and the topic....my brain has drifted towards the fluid dynamics of fractals too....and am working on how to integrate that into my art

[jehovajah]

You are Welcome .

As the new Fractalforums goes through beta testing I am gradually preparing for a new progression of this topic there. This will be left as a resource hopefully inspiring art and computational development .
I am currently reviewing Benoits own interview on his life and works.

It makes these sculptures so much more accessible.

<a href="http://www.youtube.com/v/FNap0r2XSpg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/FNap0r2XSpg&rel=1&fs=1&hd=1</a>

http://m.youtube.com/watch?v=FNap0r2XSpg
Here Sheldrake does what many philosophers do: he formalises an aspect of Fractal geometry thus killing it! Any time a philosopher mentions Platonic, they are foisting a view of Platonism that is essentially deathly. Benoit was Alice at the time and actively continuing his development of fractal Geometry. And the nature ofFractal geometry is dynamic, not only in spatial form, but in scale, in affinity and in time.
The phrase "almost self similar" is essential to apprehending a fractal dynamic and so a fractal topology or manifold. Both these ideas of dynamic and topology deeply imply trochoidal behaviour.

That. If I may be do bold, is the direction for your artistry.