“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

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

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…

“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

Volvox globator, a colonial green algae (more info at Wikipedia)

The vast majority of these illustration plates are from a plant systematics wall chart series – the Dodel-Port Atlas – released between 1878 & 1883”

via: http://bibliodyssey.blogspot.com/2012/12/plant-anatomy-charts.html

Volvox, a colonial green algae

From Wikipedia

“Volvox is the most developed in a series of genera that form spherical colonies.[1] Each mature Volvox colony is composed of numerous flagellate cells similar to Chlamydomonas, up to 50,000 in total,[2] and embedded in the surface of a hollow sphere or coenobium containing an extracellular matrix[2] made of a gelatinous glycoprotein.[3] The cells swim in a coordinated fashion, with distinct anterior and posterior poles. The cells have eyespots, more developed near the anterior, which enable the colony to swim towards light. The individual algae in some species are interconnected by thin strands of cytoplasm, called protoplasmates.[4] They are known to demonstrate some individuality and working for the good of their colony, acting like one multicellular organism.”

Image 1Volvox aureus, by Dennis Kunkel (2002): http://www.denniskunkel.com/index.php?module=search&pId=100&keyword=volvox&phrase=1

Image 2: From Wikipedia, by Frank Fox (www.mikro-foto.de); cc-by-sa

Image 3: From Wikipedia, cc-by-sa

Image 4: Life cycle of Volvox carteri: http://www.metamicrobe.com/volvox/

Ceramium spp. and a bonus Callithamnion sp. (red algae)

Image 1: Source: Algaebase

Caption: Ceramium juliae, Morris Point, Stilbaai, South Africa. 31 Oct 2001. Herre Stegenga. © Herre Stegenga 

Image 2: Source: Algaebase

Caption: Ceramium mazatlanense. Hawaii; scale 300 µm. 15 Aug 2011. J.M. Huisman. © J.M. Huisman.

Image 3: Source: WoRMS (cc-by-nc-sa)

Caption: Ceramium pallidum

Description: microscope, location: Spain, Galicia, Coruña, Pantín’s beach, 2007
AuthorBárbara, Ignacio
JPG file – 1.22 MB – 1000 x 1350 pixels
added on 2008-03-19 – 356 views
WoRMS Taxa on this image: 
Ceramium pallidum (Nägeli ex Kützing) Maggs & Hommersand, 1993

Image 4: Ceramium ciliatum © C. Romero Zarco – Universidad de Sevilla, 2003

http://www.aloj.us.es/carromzar/algas/Ceramiaceae.html

Image 5: Callithamnion sp., same source as Image 4

What does the “B” in “Benoit B. Mandelbrot” stand for?

“Benoit B. Mandelbrot”

Via that giant Reddit thread: http://www.reddit.com/r/AskReddit/comments/1h1cyg/whats_the_most_intellectual_joke_you_know/

(Whoa — according to Wikipedia, Mandelbrot “chose his own middle initial, but it doesn’t stand for anything”)

Again, had it in a folder so long I lost the source. Any suggestions?

EDIT: Saw it credited to www.users.math.umd.edu/~wphooper/frac/frac6.gif but the link doesn’t work… so probably made by W Patrick Hooper, who did his undergrad at UMD: http://wphooper.com/

That UMD Experimental Geometry Lab has some pretty sweet math images too: http://egl.math.umd.edu/projects-archive.html