User:Munin295/Random circuit

This article covers two categories of random circuits:


 * Random Number Generator
 * Generates a random sequence of numbers.


 * Random Pulse Generator
 * Outputs a pulse at random intervals.

Random number generator
A random number generator (aka RNG) is a circuit that can generate a sequence of numbers with no recognizable pattern.

All of the RNGs below depend on the stack maximums of the items they move around:
 * A 64-stackable item is any item with a stack maximum of 64 items (for example, apples, sticks, cobblestone, etc.).
 * A 16-stackable item is any item with a stack maximum of 16 items (for example, ender pearls, signs, snowballs, etc.).
 * A non-stackable item is any item which cannot be stacked (for example, tools, weapons, armor, doors, boats, minecarts, etc.).

Basic RNG
Two basic random number generators are used as components in more complex RNGs.


 * Basic 2-RNG


 * 1x3x2 (6 block volume), 1-wide, flat, silent
 * circuit delay: 3 ticks (rising) and 1 tick (falling)


 * Outputs either power level 1 or 3 while on, power level 0 while off.


 * When the input turns on, the dropper will randomly choose to push either the stackable item or the non-stackable item into the hopper, causing the comparator to output either power level 1 or 3. Because the powered dropper is a solid/opaque block, it will also deactivate the hopper, preventing it from pushing the item back to the dropper until the input turns off.


 * The output power level can be used as is (for example, to subtract 1 or 3 from a comparator in subtraction mode), but more often the output is connected to a line of two redstone dust so that the output is 0 or not 0 (to randomly power a repeater, activate a mechanism component, etc.).


 * Variations: If the dropper is powered indirectly (for example, by quasiconnecitvity or an adjacent powered block), the hopper won't be deactivated and will immediately push the item back into the dropper. This turns the circuit into a monostable rising edge detector with a 3.5-tick output pulse (still with a random power level of 1 or 3).


 * With only two items in the dropper, both output power levels will be chosen with equal probability. The probability of the output levels can be changed by adding additional stackable and non-stackable items to the dropper (which must all be different from each other so they won't stack). For example, with two different stackable items and three different non-stackable items, the RNG will output power level 1 40% of the time and power level 3 60% of the time.


 * Earliest Known Publication: 14 March 2013


 * Basic 3-RNG


 * 1x3x3 (9 block volume), 1-wide, silent
 * circuit delay: 3 ticks (rising) and 1 tick (falling)


 * Outputs power levels 1, 2, or 4 while on, power level 1 while off (but see variations below).


 * When building this circuit, wait until the hopper is deactivated by the powered dust before putting five 16-stackable items in its far right slot. Then put a 64-stackable item, a 16-stackable item, and a non-stackable item in the dropper.


 * Before the input turns on, the hopper's five 16-stackable items are enough to produce a power level 1 output from its comparator (even a single 64-stackable item would be enough for that). These five items should never be returned to the dropper, so the comparator's output will never drop below power level 1.


 * When the input turns on, the dropper will push an item into the hopper, which will be placed in the hopper's left slot. It takes 23 64-stackable items (or five 16-stackable items and three 64-stackable items, or six 16-stackable items) to produce power level 2, so if the 64-stackable item is pushed that won't be enough to increase the output power level, but if the 16-stackable item is pushed the output power level will increase to 2. And if the non-stackable item is pushed, the output power level will increase to 4.


 * The hopper is held deactivated by the powered dust when the circuit is off, and by the powered dropper when the circuit is on. But, when the input turns off, there is a brief 1-tick moment when the dropper has just turned off, but the torch attached to it hasn't turned on again. This allows the hopper to activate for 1 tick, pushing an item back into the dropper. A hopper always pushes items from its left slots first, so the hopper will push back the item the dropper pushed into it, rather than any of the 16-stackable items in its far right slot, allowing the circuit to reset itself.


 * Variations: You can remove one of the items from the dropper to create a 2-RNG with different power level outputs than the regular 2-RNG: removing the 64-stackable item outputs power levels 2 or 4, removing the 16-stackable item outputs power levels 1 or 4, and removing the non-stackable item outputs power levels 1 or 2.


 * You can add additional redstone dust leading from the hopper to a block next to it, and then down to the side of the comparator. This 2-wide variation will keep the comparator's output off while the input is off.


 * With only three items in the dropper, all three output power levels will be chosen with equal probability. The probability of the output levels can be changed by adding additional 64-stackable, 16-stackable, and non-stackable items to the dropper (which must all be different from each other so they won't stack). For example, with one 64-stackable item, one 16-stackable item, and two different non-stackable items, the RNG will output power level 1 25% of the time, power level 2 25% of the time, and power level 4 50% of the time.


 * Additional items can be added to the hopper to increase all of the output power levels.


 * Earliest Known Publication: 16 April 2013

Analog RNG

 * Analog 1d2-RNG


 * 2×3×3 (18 block volume), silent
 * circuit delay: 3 ticks


 * Outputs power levels 1 or 2 while on, 0 while off.


 * This is a basic 3-rng with the non-stackable item removed.


 * Analog 1d3-RNG


 * 4×4×3 (48 block volume), silent
 * circuit delay: 4 ticks


 * Outputs power levels 1 to 3 while on, 0 while off.


 * The basic 3-rng outputs power levels 1, 2, or 4, which is almost correct for a 1d3 RNG. To correct it, another line is added to subtract 1 from the output when it should be 4. The additional comparator is added to the output line to make sure the two lines are calculated at the same time (otherwise it would be power level 4 for 1 tick, then power level 3 as desired).


 * Analog 16-RNG
 * 5&times;8&times;4 (160 block volume)
 * circuit delay: 8.5 ticks


 * Outputs power levels 0 to 15 while on, power level 0 while off.


 * Uses four 2-RNGs to subtract 1, 2, 4, and/or 8 from 15.


 * Reducing the number of 2-RNGs reduces the possible outputs: three 2-RNGs produces an 8-RNG, and two 2-RNGs produces a 4-RNG (the exact power levels depend on the power level provided to the subtraction comparators).


 * Earliest Known Publication: 10 June 2013



Binary RNG
…


 * 1-Bit Binary RNG


 * 1×6×2 (12 block volume), flat, silent
 * circuit delay: 4 ticks




 * Close N-Bit Binary RNG


 * 1×7×2 (14 block volume) per output, silent
 * circuit delay: 4 ticks




 * Spaced N-Bit Binary RNG


 * 2×6×2 (24 block volume) per output, silent
 * circuit delay: 4 ticks



Unary RNG
A unary rng (aka "random selector") has one input and multiple outputs&mdash;when the input turns on, one random output turns on.


 * A2U RNG


 * An a2u rng consists of an analog rng, and an a2u decoder to convert the analog signal into a unary encoding.


 * Hopper-Loop Unary RNG


 * 1×5×3 (15 block volume) per output, silent
 * circuit delay: 2 ticks


 * Outputs 1 to N while on, nothing while off.


 * Deactivate the hoppers (by powering them) before putting items in, to keep the items from moving around while the circuit is being constructed.


 * While the input is off, the items cycle around the hopper loop, but the output from their comparators is suppressed by the line of dust on the output torch blocks. When the input turns on, the items stop moving and the suppression line turns off, producing a single output.


 * Variations: A zero-signal (while off only) can be taken by adding a repeater next to the first output torch, to take power from the suppression line.


 * Other unary rngs
 * A dropper pushes a random item into an item sorter. The sorted item triggers an output, then it recycled to the dropper.
 * A mob spawner spawns a mob to a random location.

Random pulse generator
A random pulse generator (RPG) outputs a pulse at random intervals.

Clock RPG
A clock RPG produces a pulse when a clocked random number generator produces an output in the correct range.

…

Update RPG
An update RPG produces a pulse when a specific block tick occurs.

Update RNGs depend on block ticks, which only occur in a 15×15 chunk area around each player.


 * BUD Random Pulse Generator


 * 1×5×3 (15 block volume), 1-wide
 * average pulse interval: 68.3 seconds, output pulse: 2.5 ticks


 * When the tripwire hook receives a block tick, it will "wake up" the sticky piston, causing the BUD circuit to activate and output a pulse.


 * Variations: The interval between pulses can be reduced by placing additional tripwire hooks within two spaces of the sticky piston. Up to 16 tripwire hooks can be placed, reducing the average pulse interval to as little 4.3 seconds (see Multiple Tripwire Hooks Table below).
 * {| class = "wikitable collapsed collapsible" style = "text-align: center;"

! colspan="3" | Multiple Tripwire Hooks Table ! Tripwire Hooks || Update Probability (per game tick) || Average Interval (seconds)
 * 1 || 0.07% || 68.3
 * 2 || 0.15% || 34.2
 * 3 || 0.22% || 22.8
 * 4 || 0.29% || 17.1
 * 5 || 0.37% || 13.7
 * 6 || 0.44% || 11.4
 * 7 || 0.51% || 9.8
 * 8 || 0.58% || 8.6
 * 9 || 0.66% || 7.6
 * 10 || 0.73% || 6.8
 * 11 || 0.80% || 6.2
 * 12 || 0.88% || 5.7
 * 13 || 0.95% || 5.3
 * 14 || 1.02% || 4.9
 * 15 || 1.09% || 4.6
 * 16 || 1.17% || 4.3
 * }
 * 9 || 0.66% || 7.6
 * 10 || 0.73% || 6.8
 * 11 || 0.80% || 6.2
 * 12 || 0.88% || 5.7
 * 13 || 0.95% || 5.3
 * 14 || 1.02% || 4.9
 * 15 || 1.09% || 4.6
 * 16 || 1.17% || 4.3
 * }
 * 14 || 1.02% || 4.9
 * 15 || 1.09% || 4.6
 * 16 || 1.17% || 4.3
 * }
 * 16 || 1.17% || 4.3
 * }
 * }


 * The interval between pulses can be increased by using multiple BUD RPGs and combining their outputs in an AND gate (the AND gate will only produce an output pulse when both or all of the BUD RPGs happen to pulse at the same time). To determine the average pulse interval of multiple BUD RPGs, multiply together their average update probabilities (see Multiple Tripwire Hooks Table above), invert, and divide by 20 to get seconds. No more than three BUD RPGs can be combined per chunk section (multiple BUD RPGs in a chunk section will change the probabilities above), but additional BUD RPGs can be combined from other chunk sections.

Design and analysis
Minecraft divides the world up into 16×16×256 chunks, and divides chunks up into 16×16×16 chunk sections. On each game tick&mdash;20 times per second (load permitting)&mdash;it executes a block tick on three block positions in each chunk section (but it might select the same block twice or even three times in one game tick). Thus, on each game tick, any particular block has a 0.07322% chance (or precisely [1 - (4095/4096)3]) to be selected for a block tick.

Many blocks do not react to block ticks -- for example, stone isn't going to do anything. But other blocks may react sometimes, or every time:
 * may grow grass (with light level 4 or more, and nearby grass blocks with light level 9 or more).
 * may spread (with other nearby fire).
 * may die (with light level 3 or less, and covered by opaque or semi-transparent block).
 * may melt (with light level of 12 or more).
 * may freeze into ice (in an ice plains or taiga biome, exposed to the sky, with light level of 11 or less).
 * Plants may grow. Of particular interest for random pulse generators are plants whose growth can be repeated:
 * growth can be recycled automatically just by placing a block next to the space the cactus will grow into.
 * growth can be detected with a BUD circuit and removed with a piston.
 * growth can be detected with a BUD circuit and removed with a piston.
 * growth can be detected with a BUD circuit and removed with a piston.
 * A will update other redstone components within two spaces.
 * A will update other redstone components within two spaces.

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