All my earlier posts have mainly concerned flash and actionscript, this time something more general:

As a starting point we have Math.random() returning a value between 0.0 … 1,0 with even distribution:

In case we want a random number more likely to be closer to like for instance 0.0, my old trick was to multiply Math.random()*Math.random, much greater odds to be <0.5.

Maths with random are sometimes very unpredictable, in the case of Math.sqrt(Math.random)) we get an – almost ? – linear curve. Function random() has a 75% change of being >0.25, so squarerooted that’s 75% for >0.5, I think:

very similar to Math.max(Math.random(), Math.random() ), greater of two random samples, with also 75% change for >0.5:

Max of several randoms seems to approach a polynomial curve, just compare Math.max(Math.random(), Math.random(), Math.random()) with f(x)=x²:

Using min instead of max naturally mirrors the situation towards 0.0.

As I mentioned this to be a bit unpredictable, when it comes to distribution random()+random() definately doesn’t equal 2*random(). In case we need randoms mainly on the mid-values, we use an average of two, 0.5*(Math.random()+Math.random()):

nice pyramid that is !

Surprise, surprise, or maybe not if you’re good at statistics and probability maths: Taking an average of even more numbers approaches the Gaussian distribution:

0.333*(Math.random()+Math.random()+Math.random()):

0.25*(Math.random()+Math.random()+Math.random()+Math.random()):

Addition and substraction gives similar results, except that naturally random()-random() is in the range between -1.0 … 1.0.

And finally a modified gaussian emphasizing the border values:

r=Math.random()-Math.random()+Math.random()-Math.random();

r += (r<0.0) ? 4.0 : 0.0;

r *= 0.25;

And the inverse 0.2/Math.random() … , well test it yourself:

… small javascript-demo for testing

Just like in the example function here, my demo shows only the values in the range 0.0…1.0, so add a proper scaling factor and addition in case you can’t see anything ! … and, hey, please comment if you come up with something interesting !

The pics in this posting were done with a code taking 20 times more samples, and a whole lot slower, than the linked demo, so don’t wonder if your result looks more rough !

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f= 0.2; r=f*Math.random()+(1.0-f)*Math.random()*Math.random(); // peak in x=f, value f<0.5

By:

Pixeleroon April 25, 2008at 8:28 am

That’s some funny coincidence – I’ve just made some very similar experiments with the BitmapData.noise() method. You didn’t by chance read the “Good Math, Bad Math” blog article about random distributions?

By:

Mario Klingemannon April 25, 2008at 7:29 pm

“Maths with random are sometimes very unpredictable”

That is totally the point! 🙂

By:

Jakeon April 26, 2008at 8:20 pm

Thanks for your comments!

Mario: Experimenting this with BitmapData.noise() – or perlinNoise()? – sounds interesting. I did already wonder how to extend and utilize this in 2D, 3D …

With google I found some older writings of ‘gaussian’ math.random, but I didn’t see ‘Good math, bad math’ earlier – thanks for mentioning.

Jake: glad I made it clear — or just confused even more ! 🙂

By:

pixeleroon April 28, 2008at 7:07 am

I was playing with noise(), but I’m pretty sure that perlinNoise() might give some interesting results, too (except that perlinNoise doesn’t give you the full range of numbers from 0 – 255).

Looking at the histogram of BitmapData.noise() with low random seeds also reveals that that the random distribution for those seeds is not as “good” as for higher seeds.

By:

Mario Klingemannon April 28, 2008at 5:44 pm

[…] various functions with different distributions for Math.random() « Pixeleroで興味深いことをやっていたのでFlashで実践。Math.random()は0以上1未満の乱数をだいたい均等な頻度で返す。じゃあ例えばこれは？ […]

By:

[FLASH]Math.random()の頻度分布on June 7, 2008at 2:42 pm

Interesting…I just learned this in probability and statistics. It’s the central limit theorem right? The more random samples you take, the more likely you’ll have a Gaussian(bell-shaped) distribution.

By:

CJ Caton June 8, 2008at 3:09 am

@pixelero: Nice work.

@CJ CAT: Well, it´s while ago since my last econometric-lessons but I think this is the point;)

By:

Flügeon September 9, 2008at 11:18 am

Pixelero, thanks a lot for publishing these functions. Very inspiring. They helped me a lot with finding more interesting ways of semi-randomly distributing forms on the digital canvas. Check out my latest experiments @ http://www.flickr.com/photos/dear_computer/

By:

Dear Computer,on February 28, 2009at 11:35 am

[…] various functions with different distributions for Math.random() […]

By:

Handnotes» Blog Archive » Random non-uniform distributionon June 25, 2009at 4:45 pm

[…] – this is also an article by PIXELERO, the article is available here: various functions with different distributions for Math.random(). I’ve also added a greyscale representation underneath to the distributions as a series of […]

By:

basics in generative art #2 : LINE « HIDIHO!on December 10, 2010at 2:12 pm

Grate one!) Loved idea, ported rendering to HTML5 canvas and modified gui a bit… hit enter on input feild to redraw=) http://jsdo.it/oleg.jakushkin/nZo3

By:

Lipricon LENONon June 8, 2011at 7:24 pm

Thanks, very nice idea of updating it to html5/canvas !

By:

pixeleroon June 9, 2011at 6:59 am

[…] one link leading most visitors to this blog is a discussion on a programming forum and that this old post of mine about random numbers is among the most popular ones. No wonder, there’s not much information about how to modify […]

By:

“How do I generate weighted random numbers?” | Pixeleroon November 13, 2014at 8:05 pm

function rndHill(skew){

let r = Math.sqrt(Math.random());

for (let i = 1; i < skew; i++){

let k = Math.sqrt(Math.random());

if (k >> param skew controls the # of Math.sqrt(Math.random())

}

return r;

}

By:

Maton June 24, 2018at 4:30 pm

sorry, some copy/paste error? Again,

function rndHill(skew){

let r = Math.sqrt(Math.random());

for (let i = 1; i < skew; i++){

let k = Math.sqrt(Math.random());

if (k < r) {r = k;}

}

return r;

}

// r = Math.min (Math.sqrt(Math.random()), …, Math.sqrt(Math.random())) – skew controls the # of Math.sqrt(Math.random())

By:

Maton June 24, 2018at 4:34 pm

Math.sin(Math.exp(Math.random()));

A slightly crazy one; no idea about application so far 😉

By:

Maton June 24, 2018at 4:37 pm

won’t fall too steep from zero:

Math.tan(Math.min(Math.random(),Math.random(),Math.random(),Math.random()));

By:

Maton June 24, 2018at 4:40 pm

[…] Pixelero 发表了一篇关于随机分布的有意思的文章。 […]

By:

《The book of shaders》学习总结 （10）生成设计 - VJ学习园地on February 26, 2021at 1:44 am