Why you can't make a Perfect Circle with Beacons in Minecraft
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- čas přidán 22. 05. 2024
- if you say it looks stupid from every other angle from the center i personally think it looks cooler. The uniformity of the completely circular pattern feels not organic enough in my opinion.
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Texture Pack Details:
Vanilla Tweaks(This affects mainly everything involved with 3D-ifying components and see through scaffolding and the Dark Mode GUI), Ph1lza’s Diamond Netherite Highlights Pack, some random netherite elytra pack you can probably find by googling.
Shader Details: I use Complimentary Reimagined, on the mod Iris Shaders. Complimentary Shaders is similar and also great.
Mod Details: [1.20.1] (MODPACK: Fabulously Optimized), Isometric Renders, owo-lib, MaLiLib, Litematica, Tweakaroo, TweakerMore, World Edit, WorldEditCUI, MiniHUD, Carpet, Pistorder.
Music: Ancient Ruins Courtyard (Slime Rancher), by Harry Mack; Mise En Abyme (Manifold Garden), by Laryssa Okada; Mall (Minecraft), by C418
0:00 - bad intro
1:08 - getting into the details
2:49 - The difficulty of circles
5:27 - How I did it
7:09 - Figuring out the colors
8:01 - final details
I actually like the fact that it looks very random from the outside, but when you stand on the center block it becomes a perfect circle. I really like chaotic designs like this and having them come together so beautifully is wonderful. I must build this in my hardcore world!
ill post the schematic of both the world and the armor stand tols in the schem channel in my discord, if you want to take it, or possibly make your own (if you have a bigger gradient)
@@squibble111 how would you get a bigger gradient? Isn't 5 glass blocks the max?
@@kr1vthere are FAR more permutations than just these 96
@@kr1v you could switch between more colors. He didn't include the values or brown. You could also reuse colors in your gradient, or do something crazy with mixing 3 colors at once
@@squibble111 I was thinking of making a muuuuch bigger circle for one of the farms im cooking and I was already thinking id have to make the datapack from scratch, but ill gladly take and modify yours, thanks!
0:43 "A baking tutorial for a cake you'll never bake" *Awkwardly turns to see my collection of recipe books*
You're not obligated to make every recipe in every cookbook
@@quantumblur_3145 Heresy
Wysi likes
Osusosuusousosus@@Aerolite_FPSwysi 727 wysi !!!!!
No but same-
you actually found a solution for the problem im trying to solve since half a year
congratulations on being the single member of the uninentionally targeted audience
It can easily be done with some trig tho
@@itripleo5780nerd
@@itripleo5780 Hush, mathematics graduate
Do the trig and get us a graph of it @@itripleo5780
I love designs that look completely random from most perspectives until you stand in the right spot and suddenly it makes sense... I am contemplating trying to incorporate this into something I can build on our SMP now :D
its like those pictures made out of lots of hanging objects. they are so cool!
copy pasta 😜
accidental?
@@kipu44 oh my god, two people that have a similar opinion! How could that happen??? Drama!!
@@TauTauofSkalgayou mean like Squibble's perspective art? :D czcams.com/video/RUBg41KUs2I/video.htmlsi=pMjevp67jfdVtPc8
@@kipu44OH MY GOD, PEOPLE HAVE THE SAME OPINION??? HOW WILD!!!
I have never watched your channel before, but I'm sold on "baking tutorial for a cake you'll never bake". The pair of rings thumbnail was pretty great too (though a rainbow beacon thumbnail would have done the trick quite well).
going rainbow beacon would have been a nice throwback to the first video, woulda looked cool. though im glad i went with this, youtube seems to like it
@@squibble111 it definitely creates the contrary assertion that brings in the clicks. But also, you deliver on it!
@@squibble111 yeah, i like that simple and technical thumbnail so it really got my attention
@@squibble111the thumbnail definitely pulled me in from the main page so i say its working
i probab;y wouldnt have watched if it was just a tutorial onb how to do that. ig why i clicked is the why behind the given diagrams. good video
It's like drawing an infinitely large 96-gon centered at (0,0), then drawing a line from the center to all 96 corners, then getting the minimum integer coordinates on that line outside a defined radius around (0,0)
The integer coordinates can only approximately touch the lines, cause most of the lines have irrational slopes, which means they never exactly hit any grid points except (0, 0)
doesn't even have to be infinitely large, it can just be big enough that the beacons all fit inside. There's definitely a way to automate this
@@HEHEHEIAMASUPAHSTARSAGA for 96ths of a circle i think a pretty decent portion if not most slopes are rational, still, you can just try to find the closest it gets to a block center within the specified radius
@@HEHEHEIAMASUPAHSTARSAGAAlthough they do get arbitrarily close, if you go out far enough
@@nddragoon I plugged the values into wolframalpha and it seems like all the slopes are irrational except the cardinal directions and diagonals (so 88 out of 96 are irrational). Though you can get arbitrarily close to any slope, it might require you to go out too far and make the beacon beam appear too small. It's an interesting question what the maximum allowed radius should be in order to make the effect look (subjectively) the best
Looks considerably better from the inside than outside, maybe thats it.
Like the Tardis. 😁
Title is partially clickbait. People assume, and rightly so, that a perfect circle refers to *world space* beacon placement when the author is talking about beacons in *screen space* (when looking up.)
@@MichaelPohoreski Yeah I was kinda expecting something like finding a best-fit radius for a 96-gon that's still fully loaded at once on a standard server. This was kinda neat anyway though.
you could probably consider how it'd look from the outside when deciding how much to space out the beacons and compromise a little bit on the size consistency without it mattering too much
@@MichaelPohoreskiwell yeah people should know that's impossible in a cube grid game
i assumed the problem was that you couldn't place beacons next to each other or something lmao 😭
so, when you explained that it was actually that the spacing was uneven i thought it was a bit silly.
BUT!!! i also completely understand the fun in solving random small problems like this so i quite enjoyed watching haha
same 😅
Same here! Turns out it was a very neat perspective puzzle.
so the conclusion is that warehouse style is the best approach to almost anything.
NOOOO sqrt 2 stikes again... disgusting irrationals. we must embrace hexagons
Hexagons, embeded with sqrts(3) all over the place...
@@Faroshkasb- but hexagons are the bestagons..
@@gallium-gonzollium even the bestagons betray us
sqrt 5 : (sad)
@@nartoomeon9378golden ratio!! :3 pentagons :333
i did a rainbow beacon in the past and wanted to make it a circle. It didn't look good due to the gaps between the beams as you explained, but i said it was acceptable since it was a single player world and no one would see this lol. I actually might reload this world and fix this rainbow beacon, to thank you for this video !
Gives the same vibe as those art pieces that are loads of bits on strings but forms a coherent picture when viewed at a specific angle
this blew my mind
omg it's crafty
blows up pancakes with mind
Dirt blocks have low explosion resistance, so that makes sense
omg its crafter counter
cop flop > crafty counter
3:24 that is actually gorgeous
It looks like a star
What I learned instead is that no two men's OCD is the same
You know had you NOT pointed out the difference in spacing I might never have noticed but now its forever going to torture me. Thank god this video also handily fixes the issue you just pointed out.
So excited this video has inspired my next two weeks of Minecraft obsession. I made a bunch of farms for beacons as my last project and then kinda stopped playing a few months back. Now I know what to do with all those beacons
This is really cool! The method you used very much reminds me of ray marching, which is typically used in rendering. It would only take a small tweak to the ray marching algorithm to turn it into a tool that does this automatically.
Oh yeah absolutely. Something I could try is spawning a shulker on each site and since shulkers snap to blocks, I can easily find the closest point to the center of the shulker
this is quite interesting. and it may be possible to calculate and assign a score to different possible beacon placements based on 1. how close the of the beacon block is to the ideal angle line, and 2. how wide the apparent beacon beam is relative to the other beacon beams
this is worth investigating, I'll have a look into it myself
Ooh, that would be really cool to design a program to do that! if you do come up with sometihing please do let me know on the discord server
Assigning scores would be a great solution instead of brute forcing! For closeness to the ideal line, it should decrease with distance, as differences in horizontal gaps would not be as noticeable at large distances I think. And for calculating apparent wideness vs other beams, you would need to know their sizes first to compare, which would make it recursive and weird. I think if you instead swap that for "distance to center", you would get the same effect, as beam width scales with radius!
Really neat math problem overall, I wonder if there could be a formula that gives a more straight answer than just computing all the values and picking the best
@@ClaraDeLemonThis leads to a diophantine equation which is unfortunately NP-hard to solve in general. However, optimization isn't too hard via a branch / prune approach, and with this particular problem you can find good bounds fairly easily that exclude all but a small number of possibilities that can be easily checked
@@JPK314 It wouldn't be a diophantine equation, as the slopes of the straight lines are all irrational, and even then you dont want to find exact solutions, you want to find approximations, which is much easier to do than finding integer sols.
I feel like this kind of thing could almost be a numberphile video. This is a really cool lesson in perspective and why the idea of "perfection" is actually very subjective. Have you ever seen one of those sculptures that looks like a big chunk of nonsense, but shining a light on one side reveals that it casts a perfect shadow in the shape of a familiar object, and then shining a light at it from another angle casts a different shadow of a different familiar object? It's a fun way of playing with perspective. This video reminded me so much of that sort of thing.
The way the circle looks careless and messy from almost any angle until you stand at the middle of the circle and it all organizes itself almost as if by magic, is genuinely an awesome thing to see play out.
I love anything that can illustrate the extent to which perception can affected shape your ideas about "reality."
Aperture Beacon Science💀
That’s awesome. While it wouldn’t be perfect, I think it might also be cool to simply increase the “thickness” of the circle, to have more beacons at each turn covering the gaps.
Edit: actually this is a stupid idea cause you’d still have the same visible gaps between some of them unless it was extremely thick
Perhaps if it is layered thrice? Though maybe it would need more.
@@vulpesinculta3478 to efficiently cover the gaps even more I think he would just need to plot more points the same way he did, but at a smaller turning increment
to increase the desnity you would have to increase the number of turns in the circle. Say you triple the number of turns, then you find 3 spots for each color (or you could have the colors repeat three times its up to the builder really). You would probably need a bigger radius to fit all of these beacons but I think this would increase the density better than making it thicker would.
@@rtrichterincreasing the number of turns would cause beacons to need to be placed even further to find ideal spots for them.
While layering the beacons wouldn't have much variation in distance.
@@martinshoosterman layering the beacons at the same rotations wouldn't have any effect. Additionally layering them would require more distance as well. You need to find a second point along that ray that is close to an integer coordinate. When you stand in the middle that coordinate will just be behind the first beam (and since its farther away it will be smaller and completely invisible from the center). Layering them at a higher frequency decreases the distance between beams and therefore "covering the gaps" which is what OPs intention sounds like.
I feel like there's a maths dessertation somewhere in there. Like you just sort of brute forced this problem with a rotating armor-stand but I bet if an actual mathematician took a crack at it they would probably be able to deduce some sort of formula that approximates a circle on a square grid in this specific way. That's what fascinates me about yall redstoneheads, sometimes you guys just end up doing incredible maths recreationally and I think there's something quite pure and wholesome about that :3
An interesting problem and a genius solution. You explained it all really well, kept it interesting, and the result was awesome (the warehouse light effect was a really nice touch). Great video all round!
Thank you !
This was... Incredible. I'd love a block-by-block tutorial on how to build this exact setup (for those of us not savvy with commandblocks :)) and I already have a plan on where to include it, but I totally get if you want this to be a ”figure it out if you can, this was my project and i want it to stay that way” thing. This felt really cool and informative and for the first ever video I've watched from you, you gained another sub
Glad you enjoyed it! Theres a WDL for everything in the discord, and you can modify things to how you please. Theres also certain programs being used in the server so you could ask around if you want to use a computer to generate things instead.
I really like this style of video where you build something useful or fun and explain it. Tbh I couldn’t care less about how quickly you could destroy a hoe but would watch so much content if you explaining things like this or like the anvil launcher that was one of your first videos. More practical mechanisms, redstone or not, are far more interesting to watch, at least for me
Gotta love how the perfect circle looks like a starting position for Conway's Game of Life.
This is such a good video. Super clever technique of approximating the best spots and a super clever solution I would have never thought of!
Amazing video! Love how you explained how you came up with the shape
You've made something incredibly epic here.
I immediately recognized the Smile Rancher ruin music too so that's awesome as well
I really like how it looks like you could put in a natural path to travel to the inside/outside of the circle, too, which I really like.
I always love seeing one of your videos come out. They’re always so unique to most other people’s. And you explain things so well. You’ve come a long way since before you even had one thousand subscribers, not that long ago, but you’re still just as entertaining, if not more
Thank you for the compliment. I appreciate you having been here since then, the channel's definitely come a long way
Very cool. Quite interesting that it looks completely random by an outside observer, but looks fantastic and evenly-spaced on the inside. Great job!
That video and the color grading one actually helped on the end barrens
I were trying to convert each discovered island in a gimmick and the island that i woulf focus on beacon messed me up when i tried to make bigger circles with degrade
Thanks, hope you get even more recognization
Your videos are so smooth and nice to watch, keep it up man!
That was awesome! Love how it all comes together in the end.
Holy moly you are an absolute genius, love ur videos, they're always not only interesting, but explained in enough depth to make even a layman like me understand the concept!! :D
You just made ray marching in Minecraft... for a beacon. You're channel never fails to blow my mind
This is something I’d likely never build, but is genuinely so cool that I can’t help but admire it.
the diagonal distance is sqrt(2), which is 41% bigger than beacons just next to each other. You can calculate the distance using Pythagoras' theorem.
yeah sure but this is not actually the angular difference. Both circles with diameter 34 and 35 can be built using 96 beacons. I'd go with 35 since i don't like double centers. you have 96 Blocks so your ideal Angular differences should be 360°/96 which is 3.75°. If you are in the middle of that circle and look south. The center of that block and the center of the block next to it have an angle of 3.37°, the next two enclose an angle of 3.34°, then 3.3° and then 3.23°, then when the first offset block comes the angle rises to 4.11°, 3.2°, 3.07°,4.44°,2.89°,4.57°,4.7°,4.76°, and then in reverse. The angles are all different.
i like this video, it's genuine and interesting and comes from passion, which you can't really say about most other minecraft videos these days ;)
ive never seen your channel nor played minecraft in a long time, but watching you engineer these solutions to such a niche problem was awesome
Congrats for the thumbnail, that was one of the most interesting videos i haven't search for
Gj
interesting build!
You mention how you rotate the armour stand 1/96th of a circle to find the next angle, but I don't think you mentioned where the armour stand starts facing.
I would guess this would be directly North, South, East or West (a cardinal direction). All the potential blocks are directly aligned behind each other, so you have the least "wiggle room".
I would guess that that this would make the best circle possible, but I might have written a code or done more maths to investigate further.
You also don't explicitly mention where the the armour stand is located. I assume it is in the centre of the block as it appears to be. This would make sense given that the end portal is on a 1 block centre.
However, I do wonder if a better result could be achieved by moving the centre. The problem I mentioned before of the blocks in cardinal direction being directly behind each other would be diminished if the centre were moved. Additionally, it is difficult to stand directly in the centre of a block, but if the player could align themselves in the centre (e.g. by walking into a corner), the player could stand in the exact centre, so perhaps get a better result.
Sorry to be pedantic. I would like to reiterate that it already looks fab.
Bunch of great suggestions. Ill never be angry at someone who cares about the details. One possible approach for alignemnt is using a minecart and dismounting, perhaps you can eject one briefly out of the ground if it wasnt an end portal your circle was centered on. Imo cardinal directionn starting point makes most sense to me because anything else would make it REALLY hard to hit those exact cardinal direction beams
Since 96/4 is 14, it should be that every 24 increments the armour stand will point in a cardinal direction anyway, so it wouldn't matter which cardinal direction you stared with. Having some alignment method would be useful, but I'd think just using a minecart would work perfectly fine. Having each 24 increments result in a perfect 90 degree turn means that you only need to solve for those 24 increments, and afterward copy the pattern to the other four quadrants. In fact, since you can divide everything into 8 lots of 12, you can solve for the first 12 increments, mirror the solution across the next eighth, then copy the resulting quarter across the other four quadrants. Then you can put more effort into making the best compromise between smallest deviation from the 1/96th increment turns and the deviation from the overall circle.
As part of that process I'd also recommend putting multiple targets down for each increment, marking each block that's within an acceptable margin of the ray. Then afterwards, choose all the targets that have minimum deviation from a circle.
@@squibble111 Alternatively, you could do the calculations outside of minecraft - write a python script or something that finds the set of 96 equally spaced rays that, for a center location either on a grid point or at a half-unit offset, get on average the closest to a gridpoint within a given range of radii. And then just output that as a list of coordinate offsets for where the beacons go.
@@patrickhector "it wouldn't matter which cardinal direction you stared with" that isn't at all what i meant. If you started 1/192nd of a revolution from north, and went in 1/96th increments, then the armour stand would never point in a cardinal direction.
On your next point: In the case of starting in a cardinal direction, you might have to pick the block for thirteen directions. (The diagonals and the cardinal directions will be shared between the eighths). If not starting in a cardinal direction, then mirroring will not work, so you can only use the order-4 rotational symmetry.
I really like the armor stand raycast. The resulting effect is really cool. I like the effect from places slightly off center, where they're not perfectly aligned but there's not an obvious grid pattern
The fact that you went so deep on this is sick. Subbed
your skybox and shaders look absolutely beautiful
OMG I’ve never heard a CZcamsr use the slime rancher soundtrack in their videos before (which is honestly criminal bc it’s actually amazing)! Great vid ❤
Cake you won't bake is a perfect analogy lol. Very small difference but a noticable one. I thought this might be about effect area usefulness but colors are pretty cool too. Good video!
incredibly creative work. excellent ingenuity. i'm following.
Awesome stuff, appreciate your honesty!
loved this whole concept but WOW that redstone circuit at the end was so cool, i have to do that for a build some day
I don’t usually watch much minecraft content but I’m glad I watched this. You are very talented, I love your building style
Wow this is detailed really good job at explaining it. Good luck to you.
Squiddy , this video has made me rethink my whole life , my wife came back , my son loves me again , my ex finally got over our breakup . Squirrel, there aren't words in the English language that can show my appreciation so I'ma just say - Thank you Pookiebear
High quality and effort put in thanks for this masterpiece
I saw the title of this video and expected some sort of "Wifies" explanation type thing, and I don't usually get interested in those types of videos, however, I was really interested in your video by the way you conveyed things. You and Gneiss Name could be a good, underrated Minecraft duo, you earned a new subscriber.
Thank you, im honored to be batched into the same group as the great gneiss name
this is a really great video my guy kudos :)
You cant because it is a game with cubes.
i think he is aware that this game contains cubes
NUH UH
This was such a relaxing and enjoyable video to watch!
Such a neat problem. Awesome video
You are right, I will probably never build this, but you made me want to and that sir is a success in my book.
Interesting video, definitely came here because of the technical looking thumbnail, I got curious. (So far my biggest finished build is like a 6×6×8 house, so kind of out of my scale)
Lovely end build, btw!
Thank you!
That was such an incredibly clever solution. Well done!!!
I have not played minecraft in years. But god I loved the math in this video. Glad you found and solved your problem :D
your solution to this is smart asf! thank you for sharing!
this is SO FREAKING COOL wow that solution with the armor stand is so fascinating
this is such an interesting problem you solved and presented the problem and solution so well.
i like your calmness, a lot of Minecraft content creators are so over exaggerating.
But you Sir, you are just doing your thing and its interesting to watch
God damn I hope you’re an engineer irl bc this is really smart. The second I saw how you used the armor stand I was like this guy is a genius.
I immediately understood the problem you were solving from the thumbnail, and I half expected to see you come up with some algorithm to precisely determine the positions. However, your method seems much more practical. Now I wonder what such an algorithm could look like, picking the number of rotations to do and determining the ideal positions that don't sit too far from the player.
I play minecraft roughly once a year nowadays, but youtube recommended this to me, and. well. huge respect!
Wow, that is incredibly interesting. Just subbed to help ya out
I’d recognize that music from anywhere It tickles my brain with nostalgia
i dont know much time and effort this took (i imagine it´s been hard) but thank you for sharing this, this is very valuable information!!!
Splendid choice of music :)
hi bronkulator
Why is this making feel so nostalgic, I think its his voice it fits the old calming Minecraft videos back in the day.
Damn this is really cool i might do something like this on my hardcore world now you inspired me
This is the most fascinating bit of information I will probably never need
I love how you overdid this but I literally can't see a difference between the two LOLLL
I like the fact you did the measurements for the whole circle, when in fact, you could have done it only for 1/8th of it and then mirror and copy it around.
Nevertheless a pretty cool video🧡
cooking tutorials for dishes ill never make are the only possible cooking tutorials for me
This is amazing and i will absolutely try to build it!
It's really cool. I appreciate your passion to solve the atristic problem with math, and the result is purely beautiful.
omgg u have a little lantern hat :3
Best thing to watch at 2am while having a mental brakedown. I'll 100% use this in my survival world when I get better
I think it would also be possible to solve it by increasing the radius of the circle, perhaps with twice the circumference, doubling each color, or leaving spaces between each beacon (if you don't have so much material), so since the blocks are further away, it would be less noticeable the irregularity between the beacons, the advantage of this is that even from the outside or not being in the center, it would be possible to see the shape.
I love the off and on sequence, it’s like a light show
that armor stand thing is a pretty neat idea. some problem solving!
This is the first video I've seen from you and the fact that other content is more redstone based doesn't surprise me after noticing that you used binary-like system for gradients.
Perfect for a end project I’m working on thanks
Just discovered this chanel, I have not played monecraft for 2 years so that cake will never get baked, but this was still an informative video. Thanks!
This is VERY interresting. And the armor stand solution is so smartly simple.
But also, the duality of man! From the perfectly spaced beacons to the ramdomly tuning on and off of them. I'm gonna admit the switching sequence not being it going perfectly around the circle slightly upsets me.
Thanks for the baking recipe, I'll do it soon enough
math time:
i think this process can be done more efficiently when using complex argand functions and circles.
starting with complex numbers:
the function [a•cis(z)] where “a” is the distance from the centre and “z” is the angle relative to the positive x axis (with a range of -pi
Thank you, you've reignited the dying flame that was my monthly minecraft phase.
This, to me, is a fascinating insight into how people solve problems in different ways. I love minecraft and redstone, but I would try to solve this with a program, probably something involving how lines intersect grid lines, which has some really elegant mathematics behind it that I've studied for a different minecraft project (for making natural-looking catenary bridges at odd angles, really fun project!)
You could solve it a separate way with computers too: Make a program that computes the sort of angle that a given point would make with the origin, test that for a whole grid of points for however big you need (maybe a 45x45 in this case or something), and then pick grid points from that list in a clever way to make sure that your grids are as evenly spaced as possible.
But neither of these are how you solved it! Getting an armor stand to send out radial lines and find this sort of heuristic solution is amazing! It's not even symmetrical in any way, but that's because it's applied to the real world even more than mine would have been! I wouldn't have even taken account of the terrain when finding a solution. As a math major, I love seeing interesting perspectives and methods that really make me think in a different way, and boy does this succeed at that. Great work!
And now i have a problem that i never had before! Hahah nice video, i love this maths games.
As a math addict and minecraft nerdy, love these little crossovers people find in the topics. Especially with minecraft! So if you find some other incredibly niche topic within this, i pray you explain it, since your explanations are great
I saw what you were going for very quickly and (not having watched your videos before) wanted to see if you would right an optimization script in code to find the optimal solution (possibly optimizing just for closeness to the 360/96 rays, or also trading off for smallest radius to reduce the effect of narrow beacon beams further away). I chuckled when it was “armor stand with particle beam and eyeball it” - very creative and much more interesting way to go about it without hardly leaving the game!