Factorizer

http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/

by espeed • 11 years ago

97 30 11 years ago

datapointed.net

espeed2• 11 years ago

Primes form a circle because they can't be divided.

Retra• 11 years ago

You can divide circles.

espeed2• 11 years ago

Primes can't be divided.

skykooler• 11 years ago

This is beautiful!

icholy• 11 years ago

I want this to be my screensaver

S4M• 11 years ago

Nice! One suggestion: allow the viewer to input a number to view directly its factorization instead of having to wait until that number is reached - although it may not be efficient if the program caches the prime numbers and factorizations. Which brings me to my second question: is the code available somewhere? The website uses a minified version of the js code. Not the most pleasant to understand the algorithm.

chrisseaton• 11 years ago

although it may not be efficient if the program caches the prime numbers and factorisations

If you watched this website non-stop for a whole year, it would still only take a thousandth of a second or so to factorise the highest number you'd reach, from scratch. Integer factorisation is only time consuming when the numbers are really really big.

gotothrowaway• 11 years ago

How do you figure out the factorizations? I've been looking for an efficient way to do this with really big numbers

waynecochran3• 11 years ago

Me too. When you figure it out try to factor 641071800653367850802176606120792275422168080497001121 for me please.

schoen• 11 years ago

This is smaller than the smallest RSA number

https://en.wikipedia.org/wiki/RSA_numbers

which was factored in 1991, so I bet you can get the right hardware and software to factor your number too. Maybe one of these implementations will do it:

https://en.wikipedia.org/wiki/General_number_field_sieve#Imp...

jwmerrill2• 11 years ago

Sure thing!

651651626268416641641703*983764598769387649827639876407 = 641071800653367850802176606120792275422168080497001121

Houshalter• 11 years ago

https://en.wikipedia.org/wiki/Integer_factorization

potatote• 11 years ago

Does anyone know what visualization library was used to do this? I am interested in learning data visualization and always wonder where to begin.

wslh• 11 years ago

Just looking at the source: http://www.datapointed.net/media/2012/10/factor_min.js and then looking at some keywords:

//Link to original minified source code http://www.datapointed.net/media/2012/10/factor_min.js

//Credits to Stephen Von Worley www.datapointed.net

Here there is an expanded version https://gist.github.com/brianahearn/6032808 and a discussion: https://groups.google.com/forum/m/#!msg/mathfuture/yEfAaey6j...

chubot• 11 years ago

Very interesting. Here is a nice explanation of the algorithm:

http://mathlesstraveled.com/2012/10/05/factorization-diagram...

(from the "About" page)

pdkl95• 11 years ago

http://www.divisorplot.com/

dedalus• 11 years ago

why a circle and why NOT a straight line which is equally plausible visualization

chki• 11 years ago

Because of the prime numbers! I always thought of them as ugly but they are actually the _complete_ numbers, which have to be represented in those beautiful circles :)

rspeer• 11 years ago

You sound a little demanding when you capitalize "NOT" like that.

I didn't make the visualization but I find the circles to be a good choice. Not only is it pretty, it makes use of two-dimensional space in a consistent way. A factor of 5 has the same shape whenever it appears.

If you factorized things into a straight line, do you just line everything up horizontally, in which case you just see hundreds of dots with gaps in them and there would be nothing interesting about the visualization? Or do you make rectangles, with some of the factors going vertically? In that case, sometimes your 5s will go horizontally and sometimes they'll go vertically, making a distinction out of nothing.

d4n3• 11 years ago

I think this actually wasn't an arbitrary choice, but a result of the algorithm.. e.g. factors are displayed as clusters ordered in a circle (factors of 2 is a circle with groups of 2, factors of 3 is a circle of groups of 3).

So for primes, you have a circle of groups of 1.

tamana• 11 years ago

They aren't circles, they are p-gons. A factorization is drawn as a tree where each level has p radially symmetric branches, corresponding to a prime factor p. (Only the leafs are drawn, but you can fill in the branches and node). A prime number has only one level

normac• 11 years ago

Totally out of left field here, but I got some auditory synesthesia from watching this, especially on high speed. If any of you did as well and are interested why, it's probably the same phenomenon talked about here: https://www.newscientist.com/article/dn14459-screensaver-rev...

bad-joke• 11 years ago

Very cool! Why does it stop at 10,000?

Factorizer

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