Visual Math

Discrete math background

    "...we try to make predictions about Nature, to anticipate what we’ll see in places we have not yet looked. If additional observations corroborate our expectations, then we’re on the right track. Several skill sets are involved: one must know how to idealize the world, and then how to work with that idealization.

Test renderings of the P22 virion EMD-1220 data set

Test renderings of the P22 virion EMD-1220 data set

 

Also see larger version of many of these images in the Volume Renderings gallery.

 

Central slice. Note the needle and lead dsDNA detail (near center), and more than four concentric shells through the horizontal plane at center of capsid.

Stereo pairs (cross-view):

P22 virion structure, EMD-1220 rendering notes

P22 virion structure, EMD_1220 rendering notes

"For a physicist, it is indeed a great joy to learn how we can use beautiful mathematics to understand the real world."  In Stephen Weinberg's "Without God" (9/25/08, The New York Review of Books)

Data source

Processing notes

Web predictions

 TED Video which speculates on the next 5000 days of the web. Infers connections between web and brain strucutre interconnectivity.

Also a nice fluid dynamics video of experiments being done on the interntational space station in micro gravity.

2x2 symmetric L-systems

2x2 symmetric L-systems

"Symmetry is a complexity-reducing concept; seek it everywhere." Alan Perlis

   The simplest 2x2 replacement systems with rules that are globally and locally symmetric.
   
    Many other types of systems also have a large number of symmetries, for example:

Alan Kay and childhood education

I've been reading a lot of material developed by Alan Kay (e.g. his writings), and others who have been influenced by Kay's vision of what operating systems and software should look like to create a revolution in the way people, in particular children, learn.

Sun god

Still fun to see an new image show up in the side bar. Pa caught my attention Mark its a good one. Seems to depict, for me, looking at the sun from underwater, while a bit drunk. Would make a good logo maybe for orange juice I particularly like the swastika origin an ancient archetypal symbol with records going to Egypt and sun god idolatry before that guy usurped it. 

Low-tech animation

Video of an interesting masking techique for creating animations.

Ambiguous cubes image

A couple people have asked to use an image of mine, 16 Rotation Ambiguous Cubes, that I am fond of. Kristel Braunius, a Graphic Designer in Holland, asked to use it in "a little book about 'clean language / communication' for the university of Wageningen in Holland." She sent the page proof (below), which is a nice juxtaposition of the image with a diagram of the human visual system.

Geometrical music theory

Science 18 April 2008 Vol 320, Issue 5874 has a wonderful article about the geometry of music, how  "many musical terms can be understood as expressing symmetries of n-dimensional space, where each dimension represents a voice in the score. Identifying—gluing together—points related by these symmetries produces exotic mathematical spaces (orbifolds) that subsume a large number of geometric models previously proposed."

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