various functions with different distributions for Math.random()

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 !