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Olivier Gerard
7,438 followers -
Mathematics, discrete or outspoken.
Mathematics, discrete or outspoken.

7,438 followers
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In answer to Antti, it is sometimes beneficial to renormalize
sequences to check if the features one imagines remain.

The first version is (A003959 - x)/x
Others are the log of this.
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2014-11-17
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Since Jess Tauber brought up recently the subject on the seqfan mailing list recently here are two variations on +Harlan Brothers' idea for finding a relation between the binomial triangle and the constant e.


A) Let's consider the limit of the n*(n-1)/2 -th root of the product of all binomial coefficients of order n.

(see first formula image)

It seems to converge slowly to a value close (?) to e.

B) Let's consider the limit of the n*(n+1)*(n-1)/6-th root of the product of all binomial coefficients (n choose i) raised at the i-th power.


(see second formula image)

It seems to converge slowly to another value greater than 4. 

In each case the idea is to count the number of factors incorporating the variable n in the product and then applying the corresponding inverse power. 

The correct offset for the polynomials involved in the exponentials might be different from the one I suggest for best results.
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2013-09-07
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Black and White Geometric Animations
h/t to Does it Float

Animations géométriques en noir et blanc

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Aaron Swartz, JStor "disseminator", creator of DemandProgress, dies at 26

He was also instrumental in pushing what is now RSS.

http://boingboing.net/2013/01/12/rip-aaron-swartz.html
http://www.aaronsw.com/weblog/dalio

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Salt Labyrinths
Motoi Yamamoto is a japanese artist constructing large structures with cristallized salt. Among other themes, labyrinths of white salt on dark background, as illustrated here.
More on the artist's web site www.motoi.biz 

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The Geometry of plant seeds

Splendid illustrations (warning: most colors are arbitrary)

http://blogs.smithsonianmag.com/artscience/2012/11/amazing-close-ups-of-seeds/

h/t to "But does it float".

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Transportation and restoration of a 1949 programmable computer at Bletchley Park. This one was used up to 1973.

See also   http://news.bbc.co.uk/2/hi/technology/8234428.stm

I am interested to see it actually working. At the time of the BBC report, the project members say they have not run tests on it yet.

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Simple but fascinating, visual factorization of integers, in an animated film.
n dots are grouped according to its divisors, one dot added at a time, the previous dots reorganizing.

by Stephen Von Worley at Data Pointed

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Nice interactive visualization of colors by preference, perceived gender, saturation.

by Stephen Von Worley

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Polygonal forms taken by viscous fluids
By John Bush and the fluids lab at MIT.

Both experimental and theoretical, stationary figures of flows under controlled conditions, enlarging what was known possible.

Here, as an example, a pentagonal jump boundary.

With short explanations and reference to research papers, starting at this home page http://www-math.mit.edu/~bush/fish.htm.

h/t to +Paul Bourke 
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