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Mathemat-ART-ical Fract-ART Augumented with Deep Learning

I am fascinated by the combinations of mathematics and art for several reasons; one reason is that it is so difficult to show the beauty of mathematics to non-experts. As a mathematician I am often frustrated that my work cannot be understood by many people that are important to me. Using mathematics to create Read more

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On Fractal Music, Fourier Analysis and Fat Cantor Sets.

Two weeks ago Adam Neely published a mind blowing video where he introduces fractal music. This is a perfect topic for my blog as well, because it is a mixture between science and art, and this is what Bats and Seahorses is mainly after (apart from the related topic of how to lead a creative life whether in science or art). Before jumping into mathematcs, first of all, here is the video:

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Knot ornaments out of Penrose tiling

Knots generated out of the Penrose tiling

(Scroll down for more pics!)

I played around a little bit with generating the Penrose tiling and especially how to get knot ornaments out of it. I used algorithm explained at preshing.com as a basis. It generates the Penrose tiling by subdividing triangles. It has two types of triangles which are labeled red and blue and they are subdivided like this:

Image from preshing.com

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An Interactive Animation Visualising a Group Isomorphism

An interactive animation programmed in JavaScript illustrating the isomorphism from the quotient of the additive groups of reals by intergers Latex formula to the unit circle on the complex plane Latex formula defined by the formula:

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Finnish Artist Makes Progress in Geometry

When I met Sir Roger Penrose at the centenary conference of Alan Turing in Manchester in 2012 I told him that Penrose tiling is now featuring as a tiling of Keskuskatu, a central street in Helsinki, he was upset. He said “They should always ask me before they use it!” I was a little dumbfounded. “Can you show a picture?” he continued. I googled it with my smart phone and showed him:

He stared at it for 30 seconds and said “It seems alright.” Sir Roger Penrose is a physicist, mathematician and a philosopher of mind. His ideas are often controversial. He believes that Gödel’s incompleteness implies that the human mind cannot be simulated by a Turing machine which in turn would imply that the human mind radically depends on quantum mechanics which in turn… requires revision according to Penrose, who doesn’t believe in the Schrödinger’s cat. Despite being controversial, he has written numerous books which are excellent at popularizing mathematics, physics and philosophy of mind thereby attracting numerous students to these areas whether they agree with him or not.

[EDIT: I have now heard that Penrose was asked for the permission about Keskuskatu and he gave one. Apparently he either didn’t remember that or he didn’t realize it was the same thing.]

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