On Sunday 23 September 2012 the London Mathematical Society again opens its doors to the public as part of Open House London 2012. Last year’s event attracted over 300 visitors and is an opportunity to visit one of the many impressive buildings in Russell Square.
Find out more here.
I have been rather creative and explored an interesting Julia set. I will say that I picked it for the way it looks, rather than anything scientific. I make no claims that this Julia set is of any real mathematical interest, nor that it is related to any interesting dynamical system or anything like that.
Here is part of the Julia set for \(F_{c}=(1 + \sin(z) ) \log(|z|)\) and with \(c = – 0.5 i + 2 \). I have included grid lines to help us navigate.
So, let us have a closer look.
The self-similarity in this Julia set is quite striking. the generic features here are also quite generic; the branching off and swirls.
Above is my attempt at creating the famous Barnsley fern [1]. It is one of the better known examples of a self-similar set, the other key example is the Sierpinski gasket.
The Barnsley fern resembles real species of Asplenium ferns, see below.
References
[1] Michael Barnsley, Fractals Everywhere, Boston, MA: Academic Press, 1993
Links
Wikipedia entry on the Barnsley Fern
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Joseph Louis Lagrange 1795 |
Just for fun I though I would have a look at some Julia sets with random noise. So I decided to have a look at the Julia set for \(F_{c}= \exp(\frac{z^{2}}{2})\) and \(c = 2- 0.5I\). This was chosen for no particular reason.
To this I modified the algorithm to include some noise in the form of a random complex number. The random number is of the form \(R_{\#} = \frac{z_{R}}{\#}\)
where \(|z_{R}| \leq \sqrt{2}\) and \(\#\) is a real number that scales the random number.
Basically, as the random numbers become larger then the fractal pattern gets “dissolved” in random noise. I won’t claim there is any real scientific value in this experiment. Enjoy the pictures.
Here we have no noise. As the pictures go down the noise increases.
My application to join the International Association of Mathematical Physics (IAMP) was successful. I received a letter via email on the 20th July 2012 stating this. I am now an ordinary member of the IAMP.
The International Association of Mathematical Physics (IAMP) was founded in 1976 in order to promote research in mathematical physics. The Association invites mathematicians and physicists (including students) interested in this goal to become members.
http://www.iamp.org/page.php?page=page_start
The International Congress of Mathematical Physics (ICMP) is organised by the IAMP, the next congress is in Aalborg, 6-11 August 2012.
Follow this link for more information about joining.
Links
As some of you will know, the Newton Institute at Cambridge is ran the programme “The Mathematics and Applications of Branes in String and M-Theory” this year.
Professor Grenville Davey is the artist-in-residence for the duration of this programme.
Grenville Davey’s sculptural work has long been concerned with relationships, familial resemblances and pairs. Through his previous residency at Queen Mary, University of London and in collaboration with Dr. David Berman (a string theorist in Queen Mary’s School of Physics), his current work continues along these lines but is now inspired by notions in T-duality and mirror symmetry in string theory where there are surprising pairings of objects.
http://www.newton.ac.uk/art/gdavey/
On Tuesday 10th July 2012 18:00-19:00, there is an open free public event in which Dr. David Berman and Prof. Grenville Davey will discuss their collaboration.
What is certainly good is that string theory and M-theory has started to permeate culture. Mathematics and physics is part of human culture. Mankind has a drive to understand the workings of the Universe, thus we have science. It is nice to see that string theory has influenced artists. This is rightly so as art should at least in part reflect the society which created it. There has been a lot of effort in understanding strings and branes, rightly or wrongly, and thus it makes sense that artists should take some inspiration here.
One thing is certain, science fiction writers have taken a lot from modern physics, and to some extent the converse is also true. I do not see why we cannot have a similar situation with more traditional art forms like paintings and sculptures.
On a personal note, I would like to try a similar collaboration with an artist myself. Being paid as a mathematical consultant for the role would be great. That said, my wife is a bit of an artist and as such I should make an effort and work on something together. If anything comes of it I will make it known via this blog.
Links
The Mathematics and Applications of Branes in String and M-Theory
The evidence that was presented at the 1954 inquest into Alan Turing’s death, which concluded a suicide verdict, would not stand up today according to Prof Jack Copeland. The story is tragic and romantic, but is it true?
The accepted version of events is that due to the persecution he was suffering as a result of his homosexuality, he took his own life by eating an apple laced with cyanide.
We have… been recreating the narrative of Turing’s life, and we have recreated him as an unhappy young man who committed suicide. But the evidence is not there
Prof Jack Copeland, University of Canterbury, Christchurch, New Zealand
By today’s standards the investigation was poor. For example, the apple was not tested for the presence of cyanide. Turing’s behaviour before his death appears not to be out of the ordinary. He was in the habit of taking an apple to bed and even left a note on his office desk, as was his practice on Fridays, to remind himself what needs to be done upon his return to work.
A motive for suicide is clear, but the pre-meditated intenion is missing.
Link
Science Community Representing Education (SCORE), which is a collaboration between several science organisations, published a report on the 27th April which analysed the type, extent and difficulty of mathematics within the 2010 A-level examination papers. The focus was on preparation for undergraduate degrees in the three sciences – biology, chemistry and physics.
Our findings are worrying. A significant proportion of the mathematical requirements – put in place by the examinations regulator, Ofqual, for each of the sciences – were simply not assessed and, if they were, it was often in a very limited way and at a lower level of difficulty than students will need to progress to degree level or into relevant employment.
Professor Graham Hutchings, Chair of SCORE
Links
The report can be found here (pdf)
