Ooh risky title yet highly attractive

*Breaking Bad: Minecraft Edition*

Mojang: "Fine, have your farms. But you're going to work for them."

“Doesn’t allow any light through but you can see through it” The scientist in me died a little inside when I heard that. The mob farm builder in me cheered!

"Doing the Chrystal Math" That cracked me up haha! Edit: the pun was honestly not intentional hahaha

Never been so wrong in my life thinking ill never use Poisson distribution XD

What if they made it so that noteblocks above the amethyst blocks make the magical chime sound

I feel like mojang just waits to see what ilmango does with the snapshots to see what they need to fix. If there is a bug or exploit or farm, he will find it.

I remember studying Poisson distribution in stats in Uni. Always thought I'd never see it again and YET HERE WE ARE. Of course it was a ilmango video lol

JESSE WE NEED TO FARM THE AMETHYST SHARDS

You had me at "poisson".

The guts on this man, calling his video "doing the crystal math"

I personally like the budding amethysts not being movable because it means every amethyst farm is going to be unique

Ilmango we know you havent been sleeping please get some sleep there is plenty of time to work on the 1.17 update

"Say my name" "You're Ilmango..." "You're God-damned right"

For those that want more math to fry their brain, here’s a more exact derivation of Ilmango’s solution to the optimal length of time for a clock-based amethyst farm: Let r be the average rate in growth stages per minute of an individual amythest (as derived in the video, 1/r is about 34 minutes) and let t be a length of time in minutes representing the length of time for our clock. Then rt is the average number of growth stages we expect to see from that crystal over the time interval. The probability of there being k growth stages for an integer k≥0 is well approximated by a Poisson distribution as Ilmango mentioned. Thus, the probability of the crystal going through (at least) 4 growth stages is approximately p=1-e^(-rt)•(r³t³/3!+r²t²/2!+rt/1!+1). Let n denote the number of exposed crystals (Ilmango took n=100). The expected number of amethyst shards dropped by any individual crystal is 4p since each mature crystal drops 4 shards, so by the linearity of expectation, the expected total number of shards dropped by all n crystals is 4np. Then the average number of shards generated per minute is given by y=4np/t=4n(1/t-e^(-rt)•(r³t²/6+r²t/2+r+1/t)). We want to find the value of t which maximizes y. Ilmango did this by calculating values in excel and looking at which t value gave the biggest y value, but we can be more exact. The maximum occurs when the derivative y’ is 0, so computing the derivative, we see 0=y’=4n(-1/t²+re^(-rt)•(r³t²/6+r²t/2+r+1/t)-e^(-rt)•(r³t/3+r²/2-1/t²)). Rearranging some terms, we get e^(rt)=(r⁴/6)t⁴+(r³/6)t³+(r²/2)t²+rt+1 which does not have an elementary solution (in terms of roots and logarithms), but using a calculator to find where the two expressions intersect, we derive t=166.61427 minutes or t=199937.13 ticks which round to 167 minutes and 199937 ticks respectively. So to be more exact, an optimal clock would harvest the crystals every 199937 ticks, although the difference of half a minute won’t make that much a difference. There was one approximation made here when we used the Poisson distribution. To be perfectly exact, we could ditch the Poisson distribution altogether since it is only the limiting distribution of the binomial distribution. Instead, the probability that a single crystal will reach full maturity in m ticks can be calculated explicitly using the binomial distribution. Using calculus to maximize this expression, one finds that the maximum occurs at m=199937.01 ticks which rounds to 199937 ticks again and is less than an eighth of a tick of difference from the Poisson approximation. Since expectation is additive, this is the optimal time length for a clock-based farm for multiple crystals as well. tldr; if you want to be super optimal, the best possible clock-based crystal farm harvests the crystals every 199937 ticks. Edit: I should add that an exponential distribution works equally well in place of a Poisson distribution.

He did the math, he did the crystal math. He did the crystal math, it was a gemstone smash.

Title caught me off guard 😂😂

I really like how Mojang made it so that Crystals are farmable, but you can't copy and paste the design. Also amazing work Ilmango!

Alternate title: Minecraft community ruins joke by repeating and explaining it 100 times in the comment section AGAIN

Me, relaxing on a Saturday morning: ilmango upload, sweet! Ilmango: *PoIsSoN dIsTrIbUtIoN*

It would be really mechanically interesting if they couldn't generate on regular amethyst blocks but could continue growing. This would mean you could push the smallest stage off onto them and it would make farm designs cooler.

8:52 when you leave a lot of white space on your sheet, because you're planning on building a numbers farm

I gotta say, the fact that you can't move the budding amethyst blocks IS pretty annoying, but it also spawns a bunch of very interesting engineering considerations. Clock or detection? How to build your detection system to allow as many crystals as possible to be detected? Every single amethyst farm will be unique, because of the random arrangement of the budding blocks. Also, the geodes seem quite common. So for worlds made after 1.17 you would certainly be able to find a geode in the spawn chunks and set it going there fulltime. Possibilities + difficulties together are what make redstone interesting. The engineer's soul cries out for perfection - but the greatest beauty and depth comes out of the strife between that desire for order and the chaotic nature of the world.

ANNND ITS HERE THE GENIUS OF MATHS AND INSANE PROJECTS I WAS WAITING FOR THIS ❤👌👍😀

15:11 had me stopping for a sec

The title sounds like a crystal meth joke I didn’t know Walter white was a KZfaqr

Maybe the sound of the goat's horn or (right pitch that came out form note block ) will shattering a crystal when exposed to a musical tone of the right pitch (its resonant frequency) . Maybe that's why they don't release for BE yet .

I wonder how much of this research will be rendered useless when the feature is actually finished in 1.17

So we have crystal math and Poisson distribution. This cracks me up ;)

Another great video! I love how you explained the poisson formula in depth, really doing the crystal math. 😆

Well done! I was trying to think what distribution to model the crystals before you mentioned it. I hadn't heard of that one.

Crystal Mat- KZfaq: DEMONETIZED

Ilmango: Doing The Crystal Math Also Ilmango: saw his chance and took it

I had flash backs to my stats class when he said Poisson distribution..

I think the best way to try to cover all 6 sides would be to have the observer and piston in the same plane for the 4 side blocks, probably with the pistons pushing to the side to collect the drops in the corner, at least for the ones where below would be covered up by the mechanism to break the bottom.

I think I might of missed you saying it, but even with using pistons your gonna have to manually replant it all right? All in all it seems like raiding geodes for blocks is better but then you can use shards to make tinted glass so farming will be needed! Good video, thanks :-)

originally didnt feel like watching minecraft stuff today, but that pun attracted me to this video, well done

This is honestly both entertaining with the title and very educational. Nice job!

I feel like you could also use Markov Chains to derive the math, and I feel like you'd be able to get slightly tighter bounds that way.

From the creators of "Breaking Bed" comes "Crystal Math"!

me: I'm never going to use poisson distribution againnnnn ilmango: buttt the crystal mathsss

This was enormously interesting. Thanks for doing the math and making the video, well done.

this was so intriguing !! cant wait to see if there'd be any changes to the crystal growth mechanics in the future update

I see what you did with the title, Ilmango

To explain what he's saying more simply: the more of budding amythist blocks you have, the better it is to use a clock based design.

Cool breakdown. Thanks for another great video!

Banger vid mango keep up the good work!

I mean if you would want the Excact optimal time, you would make a function for how many per hour for a cycle lenght, take the derivate, =0, and find the right one.

Thanks now we are all in FBI's watch list

I cannot but admire such dedication! Awsome :D

Got flashbacks to my uni statistics classes. Great video keep it up!

Lol I can imagine ilmango laughing at the pun in the title but conflicted as to whether he should risk putting it in or not. Looks like it was too tempting

You now a far is good when it has a spreadsheet and it matches the expectations

Good to see the technical stuff! :D

If skulk sensors don’t trigger when they grow you can just have a bunch of pistons with sensors on top positioned to break them. Have a dispenser on a clock to fire a snowball at regular intervals with a bunch of hoppers below the whole thing to collect them. If sensors don’t break in water then you might be able to run water over everything to flush the shards, though you probably won’t be able to hit all of them because of unlucky positioning

Lol my brain was trying so hard to read the title wrong Good stuff mango

For a second there I thought it said “Doing the crystal meth” in the title

Newspaper: "Ill mango overdoses on purple crystals"

Beautiful video shows how much you can figure out with relatively simple math

I literally had the Poisson distribution like a week ago in school, and here i am, finding it on a Ilmango video

Ilmango: geo odes. Everyone else: GEO ODES!

I really appreciate you showing the timings for the clocks! Tip for anyone building a farm: Set your pistons from the top of the geode down and then put your clock in. Water streams or minecarts to collect. Super simple just really tedious.

I think the detection, pushing and manual harvest method could be interesting. With an isolated bud, and four sides covered by a counter system and the bottom covered by an 11 block column. When full growth is counted, the cluster is moved down 1 block up to 11 of them on each side of the column. the 12th cluster is pushed off the end and broken if not done so by a player with fortune. The top side would need to be punched out by a clock and collected with a hopper minecart or something. Since a player is checking on the system anyways the very low chance that the counter breaks would be found and fixed. I also think that a hopper dropper counter would be more compact.

I can't believe I'm going to say this but I deffo would watch Ilmango teach me math

bruh i was just studying the poisson dist in my stats course

Excellent work with the math and the testing o/

Loved the video, thanks for showing the math :)

His obsession for farms has got him insane.

the way i see it ya could use the detection system and a longer clock system, for the off chance that there is a double growth, even if the detection system stalls it would reset after 1 unsuccessful breaking after the stall... maybe individual clocks for say up to 6 budding amethyst block that would reset if all detection systems in that group went off in the time the type of farm for this is really interesting and very difficult to estimate every block to do as intended, maybe my example might help with a more efficient farm

Love the use of poisson’s distribution to figure this out. The use of true knowledge here.

I just always love the intro!

Love the title 😂

I thought it said crystal meth, and I got really curious how the hell that's possible in minecraft

I love doing crystal math! The answers are usually quite CLEAR to define.

11:25 why does all those crystals in one place looks so satisfying!

Ilmango: makes a meth joke Me: a surprise to be sure, but a welcome one

and what about using upcoming sculk sensors? crystals make sound when they grow i think?

here in Colombia we got a Doritos ad that had the same music that ilmango uses in his intro, I couldn't see that ad without thinking of ilmango

I appreciate the effort that went into this video.

Lol the title had me laughing for years 😂😂

7:26 why not metric testing?!?

great video, its clear that a lot of time and effort were put into it!

Love that you used Poisson Distribution to find the optimal harvest interval

“Doing the crystal math” sounds like a certain drug lmao

I read "doing the crystal math" as "DOING CRYSTAL METH" LMAO

Big props for doing the maths!

I just finished my homework for my statistics class. So when you started talking about your optimization problem and poison distributions I had PTSD flashback.

Alternate title: doing the crystal met-

I misread the title as "doing the crystal meth"

Titles like this are a good enough reason to like, even if they weren't attached to such great videos.

So, I had a simpler idea. What it would need is a couple of hoppers, an Observer, and a piston along with a comparator, redstone dust, and a repeater. You set up the observer to detect an update of each time the amethyst grows one stage and it shoots an item out of the dispenser into the hopper which is next to a comparator that's connected to Redstone dust which leads to the repeater that'll set off the piston when the signal is at full strength(when the amethyst is able to be obtained properly) which sets off the piston, breaking the amethyst and making it go into the second hopper which would lead int the farm's chest

Minecraft Breaking bad edition.

Please tell me "doing the crystal math" was on purpose That title is beautiful

Beautiful video - bravo.

Ilmango Amethyst blocks can be used perhaps as flooring to avoid people getting away from Skulk Sensor... So it isn’t just used for decoration...

Ilmango: "1.17 Shard Farming: Doing The Crystal.." FBI: "Hmmm" 🤔 *Open phone* Ilmango: *"1.17 Shard Farming: Doing The Crystal Math"* FBI: "Oh Okay"

I can't be the only one who read the title as "1.17 Shard Farming: Doing Crystal Meth".

what a great video! Loved it

i followed your calculation and plugged the derivative to obtain the minimum. (using Autommatic differenciation and a newton-raphson solver). The exact number is 166.6138649314744 minutes, or around 166 minutes and 36.83 seconds. i love the content!