Math

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.

—Jean le Rond d’Alembert

 


“Figure 1: Left panel: Chaotic attractor of a driven anharmonic oscillator on the location-position plane of a stroboscopic map taken with the period of the driving. Right panel: Natural measure on the same chaotic attractor. Lighter colors indicate higher local values of the distribution. Both the attractor and the natural measure are fractal. (From T. Tel, M. Gruiz, Chaotic Dynamics, An Introduction Based on Classical Mechanics, Cambridge University Press, 2006, with permission.)”

Via Scholarpedia:

http://www.scholarpedia.org/article/Attractor_dimension

Diagram by Edward Ott, Scholarpedia:
http://www.scholarpedia.org/article/Basin_of_attraction

Figure 1: (a) Double well potential V(x) , and (b) the resulting basins of attraction.

Image 1: Basket stars (Gorgonocephalus) SERPENT project (img source)

“These basket stars were observed offshore Norway at the Midnattsol field. They are at the top of a ridge on the seabed at 928m depth using their branched arms for filter feeding in the strong currents.

archive.serpentproject.com/1107/ ”

Image 2: Basket star (Gorgonocephalus) SERPENT project (img source)

“This basket star was observed offshore Norway at the Midnattsol field at 928m depth. You can see a big close-up of this creature at http://www.serpentproject.com/magnify_gorgon.php

archive.serpentproject.com/1107/ ”

Image 3: GorgonocephalusSERPENT project (cc-by-nc-nd)

That second one has its mouth facing up — there are photos out there, but watch out — it’s nightmare fuel! (see also: Sarlacc)

Via this excellent photoessay!
http://echinoblog.blogspot.com/2013/01/a-galaxy-class-of-gorgonocephalus.html

(Sarlacc comparison from this post)

Image 1: Basket star (Astroglymma sculptum). Teresa Zubi, 2005 (source

Image 2: Giant Basket Starfish (Astrophyton muricatum) juvenile on Common Sea Fan (Gorgonia ventalina) Belize. Chris Newbert (source)

Image 3: Crystalline Entity encounters the Enterprise-D (comparison made in this excellent photoessay)

More info: http://echinoblog.blogspot.com/2010/01/gorgonocephalus-because-weird-is-what.html

I don’t know what to call this pattern, but I like it!

Image 1: “The Maze” by Debralee Wiseberg (link and another gallery)… I think it’s corroded metal?

Image 2: 2,2-(Bipyridine)(Naphthalene)-fusion melt (25x)

Herb Comess. Honorable Mention, 1994 Nikon Small World Photomicrography Competition (link)

Gorgonocephalus eucnemis, a species of basket star (starfish) from the Arctic

Photo by John Rix: http://www.flickr.com/photos/fathomthis/1795586640/

Basket Star reaching into the void (Gorgonocephalus eucnemis)

Queen Charlotte Strait, BC, 7 Tree Island, 2007

http://www.fathomthis.ca/simple_gallery/print_gallery.html

More info:

http://echinoblog.blogspot.com/2010/01/gorgonocephalus-because-weird-is-what.html

http://en.wikipedia.org/wiki/Gorgonocephalus_eucnemis

(I dressed up like a basket starfish last Halloween!)

Moravec bush robots! A design for fractal branching ultra dextrous robots, proposed by Hans Moravec:

http://www.islandone.org/MMSG/HansMoravecRobotBush.html

Image 1: Woefully unsourced! Clipped from a scanned PDF, more than likely… possibly from Mind Children by Hans Moravec?

Image 2Moravec, Hans; Easudes, Jesse; Dellaert, Frank (1999). “Fractal branching ultra-dexterous robots (Bush robots)”. NASA Advanced Concepts Research Project. PR-Number 10-86888.

(Wikipedia on Bush robots)

Adrift in Space Time, by Jason Padgett

http://fineartamerica.com/profiles/jason-padgett.html

Jason D. Padgett is a number theorist with Acquired Savant Syndrome from Anchorage Alaska, currently living in Tacoma Washinton. The beauty of numbers and their connection to the pure geometry of space time and the universe is shown in his fractal diagrams. 

All are HAND DRAWN using only a pencil, ruler and compass.”

http://fineartamerica.com/featured/2-adrift-in-space-time-jason-padgett.html

http://abcnews.go.com/blogs/health/2012/04/27/real-beautiful-mind-accidental-genius-draws-complex-math-formulas-photos/

After being kicked in the head repeatedly during a mugging:

A scan of Padgett’s brain showed damage that was forcing his brain to overcompensate in certain areas that most people don’t have access to, Brogaard explained. The result was Padgett was now an acquired savant, meaning brilliant in a specific area.”

shawnkthompson:

Following a head injury, Jason Padget developed extraordinary mathematical skills and a weird form of synesthesia that allows him to see the fractal reality.

According to the artist’s profile, 

“All are HAND DRAWN using only a pencil, ruler and compass.”

http://fineartamerica.com/profiles/jason-padgett.html?page=1

http://abcnews.go.com/blogs/health/2012/04/27/real-beautiful-mind-accidental-genius-draws-complex-math-formulas-photos/

After being kicked in the head repeatedly during a mugging:

A scan of Padgett’s brain showed damage that was forcing his brain to overcompensate in certain areas that most people don’t have access to, Brogaard explained. The result was Padgett was now an acquired savant, meaning brilliant in a specific area.”

fathom-the-universe:

Exotic Fractals

 

These images look like exotic phyto-plankton, but in fact they are boundary of different Julia sets.  Julia sets are mathematical fractals. The same pattern repeats infinitely in smaller and smaller detail. Following the same simple rules repeatedly, these amazing patterns are formed.

Fathom the Universe

Source and image credit: http://www.ijon.de/mathe/julia/some_julia_sets_1_en.html

 

Dude! That top one totally looks like a dendrimer! Will post more about dendrimers soon…

XXLux 

by Barbara Doser and Hofstetter Kurt, 2006

medien.KUNSTLABORKunsthaus Graz

Caption:

A screening of ecstatic moments created with the Video Feedback technique at the event horizon of perceptible worlds of image and sound while generating a moving picture. Moments distilled from experimental videos and compiled into a new unit.

Video Feedback is mapping (imaging) any visual event (image) to itself through parallelism and circulation. A minimum change of its instrument positions (video camera | screen) generate a maximum of stimuli at the time-based event horizon of perception. A flood of rapidly changing abstract images on the move will be experienced as a world of spatial complexity and of dynamic states.”

Source: http://www.sunpendulum.at/parallelmedia/time-no-time-01/xxlux.html

Background info on optical feedback

“Kaleidoscope feedback,” Peter from Xinaesthetic, 2009

Caption: “I’ve been playing around a bit with doing video feedback through a kaleidoscope shader.

In these images, the ‘seed’ that is fed into the feedback is simply the plain black or white background of the window. There is a single rectangle rendered with the output of the previous frame as a texture, which is fed through a GLSL shader which inverts colour and applies a kaleidoscope effect, resulting in rich chaotic imagery.”

http://www.xinaesthetic.net/2009/10/kaleidoscope-feedback/

order and chaos, grayscale, edge of chaos, feedback, generative art, algorithmic, fractal, square, dendritic

Spirosketch necklace and bracelet set from Polymath Design Lab!

http://www.polymathdesignlab.com/made-with-lasers/spirosketch/

Available at their Etsy store