Some FAQ since this vid is blowing up haha: - You're only plotting one point at a time? Why can't you just solve the equation and go line by line? Because many equations, such as the ellipse, are not functions, and cannot be "solved". They yield multiple outputs per one input, and fail the "vertical line test" which you may remember from high school. - Why not make multiple plotters so that it can do more than one pixel calculation in parallel? This may speed up the process slightly, but not by very much. Minecraft is single-threaded, and the mod speeds up the game as much as possible. So if you had 2 plotters, it would graph twice as fast but with twice the lag, and therefore cancelling out. - Can you use pipelining to make this faster? Yes, absolutely. I never did pipelining with redstone at the time of this build, so I didn't think to do it- or at least, I didn't think it would make enough of a difference to be worth it. Looking back on this, you could increase the speed by order of magnitudes, as it's possible to create 5hz multipliers. - Method 3 isn't perfect, what about polynomials that are completely non-negative? Wouldn't that be considered all positive by Method 3 and hence no sign change is detected? Yes, you're absolutely correct. This is a rare case that I didn't realize, and it's so cool that some very smart commenters noticed this. The equation (y - 5x)^2 = 0 is supposed to look like the line y = 5x, but under Method 3, it graphs absolutely nothing as all the z values of z = (y - 5x)^2 are nonnegative. I still have SO much love for method 3, because only a very small set of equations have this property, but great catch nonetheless! I'm not sure how you would fix it, or if it's even possible in an easy way.

imagine trying to test it and having to wait hours just to see if something works

- No one: - This guy: "Hi I'm a Senior Redstone Developer"

You: "This was a crazy project" Also you: "This took just over a month" HOW DID YOU DO IT SO FAST???

As someone who is typically intimidated by coding, computer science, and redstone, this video was an absolute pleasure to watch. Your thorough explanations are much appreciated; for the first time in forever, I feel like I actually understand how one of these things works! Thank you so much, and amazing job!

Well done!

3:14 the rotated ellipse took around 29 hours to graph according to the timelapse speeds of this and the previous graph and the fact that the previous graph took 16 hours EDIT: i watched the video more and apparently he actually did say the time it took

5:35 "That's how it works on Paper, but let's see how it runs on Spigot." - mattbatwings in some parallel universe

"its thick, but thin in some parts, and still has holes in it" sounds perfect to me

Calc teacher: "Stop playing Minecraft in class!" mattbatwings: "I'm using my calculator." Calc teacher: "Class was over 90 minutes ago..."

The technical explanation was awesome! I could not figure out how to plot points without holes in the graph. I was pretty disappointed not finding the solution I’ve been searching for in your video until you said: “Now, I’ve been lying to you.” That is a very elegant solution! My calculator won’t be as efficient as yours, but it’s been fun learning how to build calculator myself! I’m preparing to build my version 4 calculator!

This is so mind-blowing! I'm in awe. Great work on both the calculator and the explanation

That is INSANE. Holy shit, I didn't know that was even possible without command blocks.

"Turing Complete" sounds really interesting when someone first explains it to you, but you can't really appreciate it until someone does stuff like this....

thanks for adding the explanation part! I'm not interested in making redstone builds but being able to do such complex calculations in such limited conditions always amazes me.

Absolutely insane how far minecraft redstone has developed over the years and props to everyone like yourself who know how to utilise it to its full potential

Watching this kind of content really makes me think about how wonderful human minds are, and there are 7 billions of them!

This man so smart, he understands everything Mumbo says in his videos

I just yesterday saw someone mentioning the “do it at the corners” Method 3 for a real computer graphics thing. It looks like you’ve independently invented marching squares. (I don’t mean that dismissively even though I can’t find a way to word it that makes that clear. It’s really cool and I don’t think I would have figured it out without that video walking me through it)

just wow!! Really liked how you explained the evolution of methods with the code example, the 3rd method is really good.

Hey I just recently finished a 4 bit calculator in Minecraft and seeing this absolute masterpiece of technology in Minecraft is not only insane but beautiful in it's own way. This may have been an older video but I'm still so impressed by your ways of pushing Minecraft to it's limits. You really are an artist and a madman at the same time. Can't wait to see what you do next!

This build is literally mindblowing. But do you want to try "multithreading"? I've done somethig like this in OpenGL with shader, where everything works async. Maybe doing a lot of counting blocks will be a lot faster?

For those that are interested, if you modify method 3 by moving the sampling points to be in the middle of each edge of the pixel, as opposed to its corners, the resulting line doesn't have those jagged edges and looks more like how you would typically draw a pixelated curve by hand. Curves also look smoother and more visually pleasing imp.

I love your method for the lines. Much more elegant than what actual graphing calculators do, which is use a floating-point step value. Imagine implementing FP math in Minecraft! 30 hours would be fast!

As someone who loves math, this is incredible, it’s like desmos but for Minecraft, the logic behind this is very interesting and intriguing. Some may say, why do this if you can just use something like desmos? But the logic and thinking behind this can be used to create part of the foundations for the logic for incredible things and to discover the Interesting and exhilarating way our world works, well done!

Amazing! Are you a Computer Science student or a prospective one? I am just starting to get into the actual Computer Science of the field learning about low level languages and how logic gates literally do everything in a computer. I am fascinated by this! It is literally just binary and logic gates that do everything in a computer, and there is no exception for redstone! Took me two years of college to realize that.

Dude ur a literal god. I’m struggling to just do simple math while you go ahead and make a whole calculator in minecraft. Crazy stuff

So you not only created a graphing calculator, you also explained how it worked and went through what you had to do to make it work? Awesome stuff.

"it checks literally every point..." Since it only uses implicit functions, would it be possible to use marching squares? That algorithm is usually a lot faster, although slightly less accurate. I mean, proper marching squares, using larger squares and drawing lines instead of just true or false.

Method 3 is really good, but I wouldn't call it perfect. It would still have trouble with a graph that gets to zero but never goes negative, like a graph of y^2 = 0. It should draw a line on the x axis, but method 3 won't. It is very fringe case though, and I have no idea how you would go about fixing it. Great video!

I can see a modified version of this being used for vector graphics eventually, phenomenal job!

Absolutely mind blowing, especially the switch to method 3

"You don't even wanna know how long this one took." That only makes me more interested in finding out.

And I assume you’re NOT going to make a tutorial on this.

this is really convenient because i recently messed around making a program to display equations on bitmaps and method 2 is what it is currently on but method 3 is really elegant and helps out a lot

its amazing how games such as minecraft can make Calculators and other complicated Machines

There’s no way in hell something this impressive, creative and mind boggling could only have 74k views. You truly deserve so much more recognition, this is so awesome to see and I’m super proud of you dude. Awesome work, I’d say more but words literally don’t work for something this massive.

In just 3 months u made a word processor, a tic tac toe, a playable tetris and a graphing calculator... All with vanilla redstone and no command blocks. Just 3 months... wtf. That's really impressive. I can't wait to see your next project, every single one of them is mindblowingly complext and you did them all in a month or less. If you can create something like this in a month... I really want to know what you can make in 2,3,4,5 months or more It would be sick if you at some point decide to make something like a plataformer game with a procedurally generated level or something like that, maybe my mind is going a bit crazy and that's a bit too much for MC and... maybe something like that would run at 1 frame per minute and wouldn't really be that playable lmao.

This is actually Useful. If you have time to wait, and want to build a serial shape, you load this. An copy the block placements.

Redstone is one of those things I've never fully understood. And the ways that people use it still amaze me. It's almost like Basic: Easy to learn, but powerful despite it being quite slow for complex tasks. Honestly this is really cool. I'm impressed.

This is brilliant! Very well done! That neighbor-checking algo for the line drawing is pretty cool :-]

Great stuff! Next challenge, use interval arithmetic and a sort of "quad tree search" in order to speed it up. That way the time complexity can be greatly reduced, although I am not sure how much overhead would be added by the additional circuitry, but it would probably be quite a bit faster for many functions :)

Wow that pixel coloring method at the end made so much sense after studying infinitesimal calculus in college 😅 Because you transformed the problem from painting a line that solves an equation to painting the edge between two zones. Thus you need to find all points for which there are two different signs in their proximity, which is the definition of an edge between areas. Though in this real world example your smallest unit is a pixel, not an infinitesimal point, so you’re able to see them.

One day notch stumbles upon this type of videos and says to himself: "holy shit... What have i created"

I don't think I've ever learned this much actually useful stuff in a minecraft video

I can't stop being impressed with your Redstone buildings :)

This is actually mind-blowing, and such little recognition? More people need to see your work, it's fantastic. I've recently been going through your logic tutorials to learn things and it's so well explained, I love it.

Woah what a genius method for number 3. Even though it requires both negative and positive values its still really good. Watching the plot I could tell it used signs somehow, but I never would've thought of that.

The way you explained this makes it seem so simple. Amazing build, and amazing explanation! Really making me wanna get back into Redstone computation!

Great video! I’m excited to see the calculator in practice! I had no idea so much thought went into the graphing. The solution you came up with is absolutely genius! This turned out amazing! 22:33 :)

How does this only have 96k views!? It's an amazing build! Your thought process in finding a viable method to display it beautifuly was very interesting I think it only popped on my feed after searching how to download games on my graphing calculator earlier btw haha

If you can put these builds in a portofolio, I think you could get hired instantly

This is so unimaginably impressive. I can't believe you did this.

That's insane. wow. Awesome! I really appreciate the graphing method explanation.

As someone with a fairly high level understanding of both calculus as well as logic gate architecture, I learned 2 things. 1: your incredibly cabale, and really know what you're doing. And 2: even with a month, you have way to much free time

TECHNICALLY you could make an instant graphing calculator by making each pixel check if it is true for its self, splitting the whole thing into 10000 smaller circuits

I can’t even begin to quantify how much binary went into this, it’s insane

Amazing machine, amazing explanation, but most importantly the graphs with method #3 look indeed perfect, much better than with the threshold method!

When you do things, just because you CAN. I love videos like this, where I think to myself "I never thought this was possible" and just watch, totally fascinated. Amazing!

that solution you came up with for the screen was damn beautiful, well done!

I respect you for wanting to do it more because you have talent, best regards from Poland

I can't find a single word to express how much i'm impressed

i know a one optimalisation trick, checking a whole line is much faster, but not usualy posible, so add a lever that would switch between line by line to pixel by pixel

these kind of extreme contraptions are starting to be funny for me. it is just unbeliveable... amazing

I don't mean to be technical, but the claim at 1:11 "It's capable of graphing any implicit equation up to 38 characters long." is incorrect. It can graph implicit functions that are on the polynomial ring with rational coefficients. Q[x] (Of course, that's for polynomials). Or more generally, the field of rational expressions F(x), on which we there exist implicit functions with rational coefficients, which arise naturally from the indeterminate X, where a rational expression is any element of the field of fractions of the polynomial ring F[x], which is also a unique factorization domain. This can account for rational functions. Edit: Actually I definitely mean to be technical, I just don't mean to be rude.

My man, this is absolutely incredible.

Very detailed and thorough explanation. So cool!

this quite literally changed my entire view of the world. wow.

Yoo I used to play on a server you ran, and forgot I subbed to you. This is sick as hell.

Ok how the hell has this guy got only 277 views atm and only 88 of them have liked it this is bloody incredible and way under apreciated

Man you must have really loved calculus a lot, not to mention, you fixated this to be somewhat a calculator, so you know the inner workings, not bad at all

You are soooo underrated, how do you not even have at least 100k subs with all this?

It's absolutely insanely beautiful

One of the most impressive redstone build so far. This is basically a working computer in minecraft.

Normal people make Minecraft on a graphing calculator. You decided to make the graphing calculator in Minecraft. Massive GG's man.

For anyone confused about why he was finding positive and negative, a positive value would mean the point is above the line, and a negative value means it is underneath. I could be wrong.

Came from reddit. I just wanted to say the algorithm you devised for filling the graph was so cool and creative.

This is really cool. That algorithm sounds like marching squares

I don't even understand how you have so much talent yet not so much subscribers. You deserve a least a million!

Just a concept: If you know if a point is to be plotted you can deploy different module to check 8 points surrounding it to check if the points fits the equation. The sensitivity for checking the next point is to be calibrated but it is a factor by which the next point is calculated. you also need a memory block to store previous position to be sure of not running into infinite loop during calculation module. So, to prevent overlapping, any pixel you have checked, set up mechanism such that it does not check for it again.

The videos I've seen lately of people doing crazy stuff with redstone... it's really come a long way since the first working redstone computer, hasn't it?

Meanwhile I struggle to make a 16 bit adder in any reasonable amount of space.

The best red stone video I’ve ever seen. Great explanation!

dude you're so smart. i dont even know how you think of all this but it makes sense

After 10 years: **Playing in minecraft in computer in minecraft**

Me in one month: builds dirt house with doorbell and piston door He in one week:

I remember back in alpha someone made a basic calculator that can only do addition and subtraction and it blew my mind. How far redstone has gone since then

Holy shit. You’ve really done it. You’re graphing quadratic equations in a fucking block game. This thing has truly blown me away. Though, as someone who’s finishing up algebra 1 and 2, I do see how complicated but easy it is to do this, at least in theory. You should also use exponential notation in the expression display. Other than that, you’ve done a great job!

That's really impressive, totally blew my mind! However, what if you plug in a function that doesn't have any points that lie on the grid i.e it doesn't have points whose coordinates are integers?

I'm pretty sure you're the person my parents compare myself to.

Great job! I love math and Minecraft watching this is so cool but it’s coolest to finally understand how the machine work, thank u for that, Good video and good job again!

The main difference between redstone and real life technology is that we can’t make redstone compacter or smaller, but in the end, literally _anything_ we’ve done in real life, is recreatable with redstone

Wow, after watching this, I feel like I actually understand why this isn't as intimidating as it looks. Still SUPER impressive.

“No matter how impossible it is, redstone can bring it to life” I dare you to push 20 blocks. Only one piston is allowed. Think smart.

bro didnt just make a whole graphing calculator but had fun doing it that really shows how much it was worth it

mattbat: calculates each value perfectly accurateley also mattbat: approximates every value to 2 pixels psssst.....marching squares

Mumbo jumbo is trembling

Disco's OCD pack is the friggin best. Very happy to see it come back in modern Minecraft

That's insanely impressive man. You could teach Comp. Orginization and Assembly 100%

I calculated and an elipse took you 1 day and 4 hours, right?