Synesthesia, Savant Syndrome: Jason Padgett, A Real ‘Beautiful Mind'

Brain-damaged college dropout became maths genius after attack | Mail Online

A college dropout has been hailed a unique maths genius - after his brain was damaged in a brutal attack by muggers.

Jason Padgett, 41, was left concussed after he was ambushed outside a karaoke club and repeatedly kicked in the head.

Now, wherever he looks, he sees mathematical formulas and turns them into stunning, intricate diagrams he can draw by hand.

He is the only person in the world known to have the skill and experts say it was caused by his head injury.

Source: Brain-damaged college dropout became maths genius after attack | Mail Online

Real ‘Beautiful Mind’: College Dropout Became Mathematical Genius After Mugging (PHOTOS) - ABC News

“I see bits and pieces of the Pythagorean theorem everywhere,” he said. “Every single little curve, every single spiral, every tree is part of that equation.”

The diagrams he draws are called fractals and Padgett can draw a visual representation of the formula Pi, that infinite number that begins with 3.14.

Jason Padgett's drawing of Pi.

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.

“Savant syndrome is the development of a particular skill, that can be mathematical, spatial, or autistic, that develop to an extreme degree that sort of makes a person super human,” Brogaard said.

Source: Real ‘Beautiful Mind’: College Dropout Became Mathematical Genius After Mugging (PHOTOS) - ABC News

Synesthesia, Savant Syndrome, Jason Padgett, Beautiful mind 314, Island of genius - YouTube

This is a hand drawn fractal. Jason Padgett, a mathematician with synesthesia (a condition where the brain interprets numbers as shapes) draws a fractal of space time at the Planck Particle size frame and at a certain frequency. Then wave equations (uncertainty) make the drawing warp and stretch as space time does from the Heisenburg Uncertainty Principle.

Source: Synesthesia, Savant Syndrome, Jason Padgett, Beautiful mind 314, Island of genius - YouTube

Related

• Jason Padgett - Fine Art
• The Fractal Maker | Neurobonkers.com
• Geek Art Gallery: Artist: Jason Padgett
• Savant Syndrome, Man sees Numbers as fractals, Beautiful Mind, Jason Padgett, Hunting dimension nova - YouTube

Möbius Objects and Animations

YouTube - Moebius Strip II 1963 Escher

Collected from: YouTube - Moebius Strip II 1963 Escher

Möbius strip - Wikipedia, the free encyclopedia

The Möbius strip or Möbius band (pronounced UK: /ˈmɜːbiəs/ or US: /ˈmoʊbiəs/ in English, [ˈmøːbi̯ʊs] in German) (alternatively written Mobius or Moebius in English) is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.^[1][2][3]

Collected from: Möbius strip - Wikipedia, the free encyclopedia

The Möbius Gear

[...]
One can think of the black portion in the image as the ring with a fixed zero input velocity. A single blue gear is a planet, and the white strip is the sun. Output can be taken either from the sun or the planets (with no regard for practicality!). In practice, however, it’s easiest to actuate the Möbius strip (the white portion).
[...]
The end result is a functional prototype, but rotating the middle ring without having the blue gears pop out is a little tricky. If you’re so inclined you can download a description of the entire process from modeling to fabrication.

Collected from: Mobius Gears

Collected from: The Möbius Gear

YouTube - Moebius gear

Collected from: YouTube - Moebius gear

Related

• Tom Longtin - Bennington, Vermont
• Make: Online | A Möbius Gear?
• http://robotics.eecs.berkeley.edu/~ahoover/CS285/FinalProject/AHoover285FinalProject.pdf

Universal Property of Music Discovered

Cognitive universal for scales : Compute Scotland

Researchers at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam have discovered a universal property of scales: if their tones are compared in a two- or three-dimensional way by means of a coordinate system, they form convex or star-convex structures.

 

By placing scales in a coordinate system (‘Euler lattice’) they can be studied as multi-dimensional objects.

Dr Aline Honingh (left) and Prof. Rens Bod (right) from the ILLC did this for nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece.

Collected from: Cognitive universal for scales : Compute Scotland

Universal property of music discovered

The many hundreds of scales in existence seem to possess a deeper commonality: if their tones are compared in a two- or three-dimensional way by means of a coordinate system, they form convex or star-convex structures. (Credit: Image courtesy of Universiteit van Amsterdam (UVA))

Collected from: Universal property of music discovered

1000 scales

By placing scales in a coordinate system (an ‘Euler lattice’) they can be studied as multidimensional objects. Dr. Aline Honingh and Prof. Rens Bod from the ILLC did this for nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece. To their surprise, they discovered that all traditional scales produced star-convex patterns. This was also the case with almost 97% of non-traditional, scales conceived by contemporary composers, even though contemporary composers often state they have designed unconventional scales. This percentage is very high, because the probability that a random series of notes will produce a star-convex pattern is very small. Honingh and Bod try to explain this phenomenon by using the notion of consonance (harmony of sounds). They connect their research results with language and visual perception where convex patterns have also been detected, possibly indicating a cognitive universal (a general cognitive property).

Collected from: UvA researchers discover universal property of music - News and Agenda - University of Amsterdam

Related

• G:/Aline_docu/documenten/JNMR_convex_scales/convex_scales.dvi - Powered by Google Docs
• A Universal Property of Musical Scales
• Music Has Its Own Geometry, Researchers Find
• Music Cognition Group, ILLC | CSCA | University of Amsterdam
• Home | Publications | Projects | PhD Students & Postdocs | DOP Homepage | About Me

Socolar and Taylor’s Aperiodic Tiling With A Single Shape

clipped from www.tilings.org.uk

How do Shapes Fill Space?

What happens when you put seven triangles round every corner?

What are the secrets of Islamic master craftsmen?

clipped from www.technologyreview.com

Thursday, March 25, 2010

First Aperiodic Tiling With A Single Shape

Mathematicians discover how to tile a plane in a nonrepeating pattern using a single shape.

Today, Joshua Socolar and Joan Taylor at Duke University announce that they have solved the einstein problem and in the process they've discovered an entirely new way to approach the problem.

"The tile presented here is the only known example of an aperiodic tile," they say.

clipped from maxwelldemon.com

Almost the 3d monotile...

Socolar and Taylor's Aperiodic monotile

Patch of tiling, the red lines show a little of the structure of the tiling. The single grey tile shows how the different pieces of the tile fit together with its neighbours.

Patch of tiling with the 3d monotile. Note how the tiles fit together at different levels.

Sources:

1. How do Shapes Fill Space?
2. Technology Review: Blogs: arXiv blog: First Aperiodic Tiling With A Single Shape
3. Socolar and Taylor’s aperiodic tile. « Maxwell’s Demon

Related:

1. Make: Online : World's first aperiodic tiling with a single shape
2. Make: Online : Socolar-Taylor aperiodic tile models on Thingiverse
3. Aperiodic tiling - Wikipedia, the free encyclopedia
4. [1003.4279] An aperiodic hexagonal tile
5. Edmund Harriss
6. A-single-tile | Products & Tech News
7. Socolar-Taylor Aperiodic Tile by Gelada - Thingiverse
8. First Aperiodic Tiling With A Single Shape | www.onu.ro

The Mandelbulb a 3D Mandelbrot Set

clipped from en.wikipedia.org

Fractal

A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"^[1] a property called self-similarity.

The Mandelbrot set is a famous example of a fractal

clipped from en.wikipedia.org

Mandelbrot set

The Mandelbrot set is self-similar under magnification [...]

Zoom animation

Regardless of the extent to which one zooms in on a Mandelbrot set, there is always additional detail to see.

clipped from www.youtube.com

Exterminate - Mandelbrot Fractal Zoom Music Video

clipped from www.skytopia.com

The Real 3D Mandelbulb

It's found by following a relatively simple math formula. But in the end, it's still only 2D and flat - there's no depth, shadows, perspective, or light sourcing. What we have featured in this article is a potential 3D version of the same fractal.

Resulting renders

But it wasn't until I incorporated proper shadowing that the subtleties of this incredible object became apparent. For the renders below and exploration afterwards,

clipped from www.skytopia.com

Further exploration of the 3D Mandelbulb

What does it look like on the inside?

Any interesting analogues to the 2D Mandelbrot set?

A 3D Mandelbrot stalk (a deep zoom inside the Bulb)

A 2D Mandelbrot stalk

A 3D Mandelbulb spiral (found at a deeper zoom inside the "Ice Cream from Uranus" picture). Click to enlarge, and see this page of the thread for how it was found.

A 2D Mandelbrot spiral

Are gorgeous flyovers and parallax zooms now possible?

clipped from www.youtube.com

Mandelbulb zoom

A zoom into the 3D mandelbulb (split in half), with full light sourcing. Enjoy.

clipped from www.youtube.com

3D Mandelbulb mountain cross sections

Over 1000 cross sections of a zoomed in section from the 3D Mandelbulb. Observe the absurdly ornate detail within. This took around a couple of days to render.

Sources:

1. Fractal - Wikipedia, the free encyclopedia
2. Mandelbrot set - Wikipedia, the free encyclopedia
3. YouTube - Exterminate - Mandelbrot Fractal Zoom Music Video
4. Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal
5. The Unravelling of the Real 3D Mandelbrot Fractal
6. YouTube - mandelbulb zoom
7. YouTube - 3D Mandelbulb mountain cross sections

Related:

1. Welcome - True 3D mandelbrot type fractal
2. Patterns of Visual Math - Mandelbrot Set
3. Skytopia - Mystery of the Real 3D Mandelbrot Fractal

Robert J. Lang The Art, Science and Engineering of Origani

clipped from en.wikipedia.org

Robert J. Lang

Dr. Robert J. Lang 1961 (age 47–48) is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has long been a student of the mathematics of origami and of using computers to study the theories behind origami. He has made great advances in making real-world applications of origami to engineering problems.

clipped from www.ted.com

clipped from www.youtube.com

clipped from www.langorigami.com

clipped from www.langorigami.com

clipped from www.langorigami.com

Like a musical composer, the origami artist works with patterns and relationships within the paper and arranges those patterns into something that touches a human aesthetic. And while complex figures must be designed according to fixed, fundamental principles (design), there is always some spark of sponteneity and serendipity (creation) in the realization.

clipped from www.youtube.com

clipped from www.youtube.com

clipped from www.langorigami.com

The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. We can group these intersections into roughly three categories:

• Origami mathematics, which includes the mathematics
  that describes the underlying laws of origami;


• Computational origami, which comprises algorithms
  and theory devoted to the solution of origami problems by mathematical
  means;


• Origami technology, which is the application of
  origami (and folding in general) to the solution of problems arising
  in engineering, industrial design, and technology in general.

clipped from www.ams.org

clipped from www.ams.org

clipped from www.ams.org

Sources:

1. Robert J. Lang - Wikipedia, the free encyclopedia
2. Robert Lang folds way-new origami | Video on TED.com
3. YouTube - Robert Lang: Idea + square = origami
4. About the Artist
5. Art
6. What's New
7. Science
8. Mathematical Imagery Presented by the American Mathematical Society - Robert J. Lang :: Origami/"Tree Frog, opus 280," by Robert J. Lang. Medium: One uncut square of Origamido paper, composed in 1993, folded in 2005, 5". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.
9. Mathematical Imagery Presented by the American Mathematical Society - Robert J. Lang :: Origami/"African Elephant, opus 322," by Robert J. Lang. Medium: One uncut square of watercolor paper, composed and folded in 1996, 8". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.
10. Mathematical Imagery Presented by the American Mathematical Society - Robert J. Lang :: Origami/"Fiddler Crab, opus 446," by Robert J. Lang. Medium: One uncut square of Origamido paper, composed and folded in 2004, 4". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.
11. YouTube - Squares-Folds-Life: Contemporary Origami by Robert Lang IMA
12. YouTube - The Amazing Origami of Robert Lang

Related:

1. OrigamiUSA
2. Apple - Science - Profiles - Robert J. Lang, pg. 1
3. The Most Interesting Origami Discussion Ever - One Man’s Blog