The Fascinating New Maths behind Minecraft Dispensers

Welcome back to what is quite possibly the coolest thing in Minecraft: differential equations. Or should I say discovering that dispenser output streams are actually a "dynamic system meaning you can use item counts to embed a binary space of a few bits, allowing you to encode boolean operations around discontinuities of the dispenser output function in a phase space of item counts," i.e. Dispenserstone and hence computation using just dispensers in Minecraft -oh wait that's for part 2.
Part 1 just touches on how I derived the equation relating prefilled dummy items to the output speed of the dispenser; serving as a delicious appetiser to the upcoming Self-sustaining Nether Tree Farm using Science video.
Also, this video was produced in part for the Summer of Maths Exposition which you can find more information about here: some.3b1b.co/
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►Links:
Custom Dispenser Output Differential Calculator: www.desmos.com/calculator/c67...
Animations Source Code: github.com/ncolyer11/Dispense...
Nether Tree Discord: / discord
Animations made using the Manim library: docs.manim.community/en/stable/
Featured Subway Surfers Clip: • Craziest Run I've Ever...
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►notes & corrections:
- The quote in this description is paraphrased from Golbemogle from the Threadstone Archive after I posted the working out describing dispenser streams using differential equations
- For those not familiar with some of the technical minecraft/redstone terminology used in this video, please refer to this explanation here: • Pulses, Clocks, Latche...
- 3:49: Explanation for what 'P' and 'F' stands for should say 'dispenser' for where it currently says 'dropper' (although I have found a way to get this mechanic to work with droppers too)
- 3:55: Here an integration variable is used in the bounds which is shorthand for first integrating an indefinite integral then substituting in initial conditions to find the integration constant
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►music used in video:
Music by Vincent Rubinetti
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/playlist/3zN...
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►cool stuff u should check out:
Awesome Farm Tutorials: / @themcarchivists
Unique Farms: • Unique Farms
Nether Tree Science: • Nether Tree Science
Fastest Tree Farm Series: • Ncore Tree Farming
My Discord: / discord
Twitter?: / ncolyer11
Patreon: bit.ly/2FbtSYV
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►Time Stamps
0:00 Problem Statement
0:48 Analysing Dispenser Behaviour
1:48 Differential Dispensers Equation
2:32 Does Item Stack Size Matter?
3:26 Solving the Differential Equation
4:30 Finding the Equilibrium Point using Limits
5:24 Calculating Items Output/h
6:11 Applying our Formula
6:52 Alternate Experimental Solution
7:08 Single vs a Range of Answers
8:00 Desmos Implementation
8:15 Closing
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#Dynamic #Systems #SoME3