Randomness and noise

Two operations about unpredictability: one different every time, the other smooth

mediumYou need: op: whole numbers and precision

rand gives a random number from zero up to but not including the one you give, and that number is fractional. A die comes out of it in two lines: first the throw, then rounding down.

steptick 0

Operation0

= rand

Operation1

= floor

Operation2

=

+

@counter0number

thrownullnull

rollnullnull

op rand throw 6 gives a fractional number below six — say 2.09; floor cuts the fraction and leaves 2; add one and you get 1 to 6, like a real die. Press “step” a few times: the throw is different every time.

The order matters here. Round rand 5 first and then add, and a six never comes up at all; take rand 7 and round it, and a seven turns up now and then. An N-sided die is always rand N, floor, add 1.

Note

Every rand is a new throw. Two lines in a row with op rand a 10 and op rand b 10 give different numbers, not the same one: rand is not a property you ask for but an action.

In the example the numbers are always the same

Press “restart” and run the example again — the same thing comes up. The game is not like that: there the generator is seeded randomly at start-up, and the same program gives different numbers every time.

Here the seed is fixed on purpose: the lesson promises numbers, the tests check them, and an example that shows something different every time can teach nothing. Keep that in mind when you move a program into the game: there will be no repeats there.

Noise is not randomness

steptick 0

Operation0

= noise

Operation1

= noise

Operation2

= noise

@counter0number

herenullnull

besidenullnull

awaynullnull

noise takes two coordinates and gives a number roughly between −1 and 1. It is not random: the same point always has the same answer, and neighbouring points have nearly the same one.

In the example the points (10, 10) and (10.01, 10) gave −0.524 and −0.520 — neighbours, and their answers are close together. (40, 10) is far away, and the answer there is quite different: 0.908.

That is exactly what makes noise useful. A random number jumps about, and anything built on it flickers; noise changes smoothly, so hills, ore patches and stains on a map come out of it — everything that should look uneven but not torn. The game draws terrain with it, and in logic it is handy for a smoothly wandering value: a speed, a delay, a brightness.

Remember

• rand N is a fractional number from zero up to but not including N.
• A die is rand N, then floor, then add 1.
• Every rand throws afresh.
• noise x y is not randomness: a point always has one answer, and nearby points have close ones.
• In the course examples the seed is fixed; in the game it is random.

Task

Make a coin: op rand r 2 and op floor heads r. You get a zero or a one, and both sides come up equally often.

Then replace floor with round and see what happens. There are now three outcomes: zero, one and two, and the one comes up twice as often as the others. Rounding to nearest gathers the whole stretch from 0.5 to 1.5 into the one, and only half a stretch each into zero and two.

A fair coin can be made with round as well, but from a different throw: op rand r 1 and op round heads r. The general rule: rand N is rounded down, not to nearest.