Fractals crack one of the classic mysteries in mathematics - Partition Numbers

[mjk1093]

http://www.eurekalert.org/pub_releases/2011-01/eu-nmt011911.php. Pretty mind-blowing stuff. I can't wait for the full article.

[jehovajah]

Me too! Reads very interesting don't it! Thanks ever so for the post!

[bib]

Thanks for posting this. Sounds very exciting. I wonder how what the mysterious P function looks like.

[jehovajah]

<a href="http://www.youtube.com/v/aj4FozCSg8g&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/aj4FozCSg8g&rel=1&fs=1&hd=1</a>

[cbuchner1]

interesting introductory lecture, but I don't see how this transforms into beautiful fractal pictures.
Extension into complex numbers, please !

[kek]

Really interesting can't wait to play with it in a fractal program!

[hobold]

I don't understand a whole lot of it. I was defeated by the partition numbers before, because I didn't recognize them and consequently didn't recognize right away that they would be too magnificent an adversary (there are optimization problems where the partition numbers are handy).

However, I think I understand enough of it to state that the fractal structure therein is much more abstract than the geometrical notion of a pretty picture which contains smaller copies of itself. Or in other words, I will have to disappoint those of you who expected that this would immediately lead to new families of pretty pictures. I don't think there is a direct way to visualize the structures that were found in the partition numbers, in images that are visually rich and detailed.

For starters, the space of positive integers (which this fractal lives in) is a line of discrete points. There is no canonical image plane to be filled with colours.

Still, very interesting and useful discovery! And an excellent presentation of the findings.

[David Makin]

Maybe the prime sequence has a fractal solution too

[jehovajah]

I don't understand a whole lot of it. I was defeated by the partition numbers before, because I didn't recognize them and consequently didn't recognize right away that they would be too magnificent an adversary (there are optimization problems where the partition numbers are handy).

However, I think I understand enough of it to state that the fractal structure therein is much more abstract than the geometrical notion of a pretty picture which contains smaller copies of itself. Or in other words, I will have to disappoint those of you who expected that this would immediately lead to new families of pretty pictures. I don't think there is a direct way to visualize the structures that were found in the partition numbers, in images that are visually rich and detailed.

For starters, the space of positive integers (which this fractal lives in) is a line of discrete points. There is no canonical image plane to be filled with colours.

Still, very interesting and useful discovery! And an excellent presentation of the findings.

For me it is not that we will see pretty pictures at first(for that i refer you to Kali's work on the reals here), but that everything we do or think in mathematics or measure with, is a fractal. Thus some fractals are boring, but they are still fractals, and we use them everyday like tape measures or like number line concepts. Incidentally this has a direct impact on the notion of continuity and continuousness, especially in relation to contiguity.

I came to this site hoping to find out and demonstrate to myself just what this has done. I knew nothing of partition numbers, and would not particularly have found them of interest to study- they relate directly to combinatorics. Now the world of maths  has changed for the better and those interested in fractals are at the forefront of that change.

Kinda reminds me of Bob Dylan's Song.

[cKleinhuis]

the earlier we teach our children chaos () the earlier we find new insights in the structures of our universe, this is one nice example that scientists
find understandings of before not understood things ...

[jehovajah]

I think, on balance i am going to include de Fermat as one of my all time greats along with Brahmagupta, Bombelli, Vieta, Napier, Wallis Newton De Moivre and Cotes, Wessel and of course Hamilton.

`it is a judgement arising out of some personal satisfaction in the contribution to what is foundational to mathematics. Many of these i list were computational whizzes, in that they could carry out for the most part an immense computation within their own heads, and remember the results, thus when computers were lacking, they could compute down to the smallest detail.

There are of course many unsung heroes in this enterprise and many who are only recently coming to be appreciated, but i cannot see any who would replace those in my list, rather i would need to extend it!

A mind numbingly boring as aggregation structure and combination may be, it nevertheless founds everything we call mathematics securely on iterative convolutions that are fractals.

Bu we can go deeper.....