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The music clip I liked the most is here.

The set to choose from here. Electronic music, purposefully fractally composed. But what about fractal-innocently composed fractal music?

Apparently, fractal-innocent visual art with fractal patterns happens: see article in Discover Magazine 2001. about “drip painting” by Jackson Pollock (1912 – 1956). It turns out his paintings display certain recursive patterns, at various levels of magnification, with varying degrees of complexity.

This prompts the differentiation between “fractal” (exhibiting unintended fractality) and “fractalized” (exhibiting fractality by design). More on sound fractalization here

Here’s also some photosounding, which according to the uploader/author exhibits fractality. The sound object is therefore fractal, not fractalized, as the fractal pattern itself is not human-generated/designed, although the image-sound translation is. Mediately, of course.

Quoting Photosounder: Various fractals and photographs found around the web turned into sounds using Photosounder. Links to the original image (when it still exists) in the annotations.

On the subject of mathematics in art and vice versa:

Couldn’t resist borrowing wikipedia’s Lissajous curve animation (shapes following    a system of parametric equations for complex harmonic motion).

credit: http://en.wikipedia.org/wiki/Lissajous_figures
The animation above shows the curve adaptation with continuously increasing $\frac{a}{b}$ fraction from 0 to 1 in steps of 0.01. (δ=0).

Max Ernst (German-born French dadaist/surrealist painter, 1891-1976), who achieved the Lissajous configuration in a couple of paintings by swinging a punctured bucket of paint over a horizontal canvas (the so-called oscillation technique, anticipating the later Pollock’s drip painting).

An article by Mike King, Reader in Computer Art and Animation at London Guildhall University, UK, with a self-explanatory title:

(2002). “From Max Ernst to Ernst Mach: Epistemology in Art and Science.” Working Papers in Art and Design 2 Retrieved <May 19, 2012> from URL http://sitem.herts.ac.uk/artdes_research/papers/wpades/vol2/kingfull.html ISSN 1466-4917

It turns out the promo image of Nora Bateson’s Bateson documentary is REAL and, moreover, of herself as a toddler and a REAL gibbon, with his arm around her shoulder (suave!!!), when they lived in Hawaii.

Click for Nora’s interview with Prof. Scott Turner:

Nora telling the gibbon story:

I love this WP commentary too:

I love being a writer. What I can’t stand is the paperwork.
Peter De Vries

The more interesting case, however, is fractality in nature. As you can imagine, the regularity is not perfect. Fractals of this sort can be found in lightnings, snowflakes, crystals, sea shells, peacock’s tails… even the common broccoli. View images I liked here

Posting below screenshot combination images of a hand and sea/plant life from the docu “An Ecology of Mind: A Daughter’s Portrait of Gregory Bateson,” which are reminiscent of fractality, in loose terms. More important is their evolutionary-ecological meaning, namely, treating shared configurations as a token of “belonging” to a co-evolving eco-system. Biosemioticians, I expect, would have a lot more to say on the subject.

An applicable description would be “nest of relationships,” used in a comics substory in the movie, where the analogs of a hand are a rose and a bunch of bananas:

Scoured from the www:

A mathematical fractal (term coined by Benoît Mandelbrot, 1975 ) is based on an equation which undergoes iteration. This derives the property “self-similarity,” which boils down to (a) recurring pattern(s), possibly on an increasingly smaller scale, which, however, preserves the configuration.

As expected, fractals by design have a definitely sci fi look–just use your imagination:

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Images produced by fractal generating software are not necessarily strictly fractal, mathematically and even to the naked eye–it is possible to zoom in on a section of the image which displays no fractal properties whatsoever.

coming up, as a follow-up on the screening of Ecology of Mind by Nora Bateson, and the discusssion at UT on the following day.

update: May 7, 2012
BTW, if no one else has come up with the term “fractality,” and one wonders why, it will have to me my coinage. Initially http://www.definition-of.net/ yielded the sequence below,

Fractality , fractality meaning , definition of fractality , what is fractality – The state or condition of being fractal .
Speech part : noun

but entering the term in the regular search box there came up with:

[No definition found .There may be a typing error or the word doesn’t have a definition in our database]