The only easy way to do it is to fill a dispenser with 4 stacks of snowballs and 4 stacks of anything else besides arrows or eggs. Put a wall in front of it and a wooden pressure plate at the base of the wall. One of two things will happen, at random, when the dispenser receives power: a snowball will be fired and the pressure plate will not be powered, or the other block will be dispensed and the pressure plate will. Obviously you could rig up as many of these as you want to create as complex of random output as is required.
The only easy way to do it is to fill a dispenser with 4 stacks of snowballs and 4 stacks of anything else besides arrows or eggs. Put a wall in front of it and a wooden pressure plate at the base of the wall. One of two things will happen, at random, when the dispenser receives power: a snowball will be fired and the pressure plate will not be powered, or the other block will be dispensed and the pressure plate will. Obviously you could rig up as many of these as you want to create as complex of random output as is required.
I've used dispensers before for a slot machine that i made, and I know how they work.
A method that is extremely random is to make a non symmetric mine-cart track with a lot of detector rails and two way corners, have these rails attaches to rs nor latches, as the cart goes around the track it will randomly turn off and on the output from the latch. underneath the track put each corner on it's own clock to switch it's direction, making it a lot more random.
Hint, do not put any detector rails near a corner, or it will lose a lot of randomness because the clock below will be overridden.
to get the output only when a button is pressed take the output and attach it to an and gate, and attach the button to that as well, then the button is pressed if the input if on the output will be on, then just make a system to turn an rs nor latch to the correct state. it's elaborate, but it ends up being almost 90% random. the larger and more windy the track makes it more random.
Its very easy actually, ignore these noobs ^.^ you put a row of any solid material, then put redstone dust on top of the row of solid block, then you put redstone torches all down the sides, then you put more stone bloks on top of the redstone torches
Look a bit like that but tnt is redstone dust, torch is redstone torch
Technically not random.. Just put a boat in a water current that loops back around to itself. Put a wooden pressure plate in front of the door so when you hit the button it shuts all the doors and then the boat stops on a plate and there's your "random" output. Like I said.. not exactly random since its going through the same loop so if you started and stopped it again immediately it'd only move one position. But as long as you don't need to worry about people hitting the button right after it started again it's random. I used this setup for a custom dungeon/maze where the exit is in one of 8 spots (can be bigger easily by just adding more plates and doors).
Depending on what you need the randomizer for that could be the easiest and most compact solution.
There is a redstone contraption that you have a bunch of quick pulse generators, then when they burn out, it is random which one will re-light. Then, you send those into rsnor latches. It is pretty complicated but "Captain Sparklez" has a video on his youtube. He uses it in a rock paper scissors game.
Does it have to be fully Redstone? Because the best way to get randomness in my opinion is to use the pseudo random events in game. Such as mob walking, Plant Growth, Item Drop, etc. Here's a thread on using chickens for pseudo randomness (Yes, I wrote it and built it, only a small part is acutally the randomizer though):
It works quite well. One chicken coop can be condensed, but the drawback with this design is unless you are in close proximity (Or have a dummy player in SMP), the chickens will despawn. This from what I hear will change in 1.8 though. Also it requires a lot of eggs to get started.
However the pros are enormous:
Leeching from Java's RNG is better than anything we could probably build in Minecraft (theirs is 48 bit I think, but I cannot remember the method (MTRNG, LCRNG, etc.)), leading to better randomness (Higher Quality Numbers).
Two chickens can be hooked up to a XOR/XNOR gate to create more random data (More movement from 2 chickens than one, causing more data, useful if you need more numbers than this thing puts out per second)
Okay I dunno if this is useful or not, just what I like. It creates very random results.
Feel free to tell me if there is anything wrong with this way...
Well the reason i wanted a randomizer was so that it could be used for a game type thing, and natural events such as mob walking and cactus dropping would not work in that sense because there may be nothing happening, so fully redstone would be needed, maybe adding dispesners
I've used dispensers before for a slot machine that i made, and I know how they work.
Hint, do not put any detector rails near a corner, or it will lose a lot of randomness because the clock below will be overridden.
to get the output only when a button is pressed take the output and attach it to an and gate, and attach the button to that as well, then the button is pressed if the input if on the output will be on, then just make a system to turn an rs nor latch to the correct state. it's elaborate, but it ends up being almost 90% random. the larger and more windy the track makes it more random.
lolwut?
YOU MUST BE REDSTONE BECAUSE YOU TURN ME ON!
Depending on what you need the randomizer for that could be the easiest and most compact solution.
Not random, torches are not random.
Nothing in real life is truely random, nevermind minecraft.
No need to say something that was already said, and yes the method the guy in question (if I'm correct about the guy) was random using torch burnout.
http://www.minecraftforum.net/topic/529469-chicken-powered-rng-v81/
It works quite well. One chicken coop can be condensed, but the drawback with this design is unless you are in close proximity (Or have a dummy player in SMP), the chickens will despawn. This from what I hear will change in 1.8 though. Also it requires a lot of eggs to get started.
However the pros are enormous:
Leeching from Java's RNG is better than anything we could probably build in Minecraft (theirs is 48 bit I think, but I cannot remember the method (MTRNG, LCRNG, etc.)), leading to better randomness (Higher Quality Numbers).
Two chickens can be hooked up to a XOR/XNOR gate to create more random data (More movement from 2 chickens than one, causing more data, useful if you need more numbers than this thing puts out per second)
Okay I dunno if this is useful or not, just what I like. It creates very random results.
Feel free to tell me if there is anything wrong with this way...