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Nautilus: Another 3x3 method

Athefre

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Nautilus

Introducing a different kind of 3x3 method. The general steps are:

1. Solve a 1x2x3 on the left.
2. Solve a 2x2x2 on the right.
3. Finish with one of several variants.

The shape formed by steps 1 and 2 can be solved using any other way. 1x2x3 then 2x2x2 is just the recommended strategy. For the variants, they range from easy to advanced. So anyone is able to get started without having to learn many algorithms. For those wanting to use a very advanced method, there are also variants for that. The variants for the method are designed to be a natural fit for the main shape formed by the 1x2x3 + 2x2x2. In particular, C33, Polar, and Transformation stand out as being natural continuations and they also have advanced options.

Pros:
  • Great look-ahead for the rest of the solve after the 2x2x2 is built.
  • Most of the solve involves the use of only the dominant hand.
  • Good for both two handed and one handed solving.
  • Rotationless.
  • Low move-count.
Cons:
  • A lot of variants. Which can be seen as good or bad.
  • It isn't always best to use r, R, U, M. Some algorithms will instead need to be R, U, F.
I recommend starting with the CLL+L5EP variant. Which would be dFR + EO > CLL > L5EP. The EO algorithms are on the EO page and the CLL and L5EP algorithms are in this variant's section on the Variants page. This variant isn't very unique anymore now that many methods end with L5EP. Although MI1 and this method were the first ever methods to have ended with that step. In this case though, there is a lot that can be done with the blockbuilding to allow for multiple L5EP angles. Things like having the empty square on B or R or using U+D L5EP or U+FR/BR L5EP. More about that is explained on the site. This variant will get you used to the blockbuilding of the primary shape and also get you started in learning how to take advantage of the open slots on the M and R layers. You could also start with one of the LL/ZBLL/LSLL variants. Again, not very unique but introduces the blockbuilding style.

Moving on after that, the rest of the variants are where the method really shows its differences among other 3x3 methods. These allow the user to keep the freedom provided by the empty square and also give the opportunity to learn simple and advanced algorithm sets.
I'm actually re-introducing this method, with a new name. This method is both new and old. I originally developed and proposed this almost 15 years ago in Fall-Winter of 2006 but have recently re-developed with a few new variants. It started with the MI1 method that can be seen in my signature. That method has a similar shape, except the DR edge isn't solved as part of the primary shape. I didn't like the ergonomics of the method occasionally requiring S moves and it also wasn't very suitable for good variants. So I decided to solve the DR edge as part of the first step. It then became a method of its own with a series of variants. Back then I had the CLL+L5EP, LL, ZBLL, and LSLL variants. Additional, more unique variants were added starting late last year and can be seen on the website.

Since 2006, there have been a few methods proposed that are similar. Most notably the very cool M-CELL method, which solves a 1x2x3, 2x2x2, the FR edge, then finishes with L5C and L5E. There is also Speed Heise-2 which solves a 1x2x3, 2x2x2, EO+DF edge, then the Speed Heise LSLL method. That is very similar to the LSLL variant of Nautilus. I'm sure there are others that have been mentioned in the New Method topic over the years. There are also other methods now that end with L5EP (which originated in MI1 in 2006). However, there is so much more potential in leaving the dFr square free. It provides a lot of freedom to work with the M and R layers.

An interesting thing to think about is that there are methods which solve the left side 1x2x3 then solve either the DF+DB edges or the right side 1x2x3 with EO mixed in at some point (more about that here). But with Nautilus, it is kind of 3D with blockbuilding being performed simultaneously on the M and R layers and EO at any point.

Check out the website and let me know if you have questions, suggestions, or variant ideas. Several algorithm sets have been generated so far. But there is still work to be done for the advanced variants and for discovering more about the method.

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Athefre

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Could you provide some example solves?
Sure, I can add examples. Though on the site there are some examples for the first part of the method. That is the most important thing to be highlighted in an example. For other steps, the example would only be representative of whatever algorithm case happens to occur in that scramble. But I can just add the continuation to those and note what variant is being used.
 

Mathsoccer

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Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!
 

BenChristman1

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So I’ve been messing around with this a tiny bit. From the 12 solves that I’ve done, I have a 44 average of 12. (I average about 16.5 with CFOP.) I also got a 19 single that was basically Petrus, so I’m not going to count that. I’ve been doing FB > 2x2x2 > DB edge > RB square > EO > last slot > 2-look CLL > L5EP. This definitely isn’t the best way to do it, but with the algs that I know now, it’s not terrible. I think that this method has a lot of potential, and I definitely think that globally sub-30 is possible with just a few days/weeks of practice.
 
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Athefre

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Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!
The number of algorithms for the variants that have been generated are mentioned in that variant's section and also for a couple of others. I guess I could specifically highlight that somewhere if that is what many desire. I am purposefully not providing the average move-count. This is due to recent methods using HARCS program numbers as representative of what humans can do. This has misled some members of the community and slightly altered expectations. Additionally, even if I did try to provide an exact number, it is actually impossible for that number to be perfect. I will say that the average movecount of most variants of this method will be around the same as Roux. More advanced variants will average 3-4 moves fewer.
 
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trangium

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The number of algorithms for the variants that have been generated are mentioned in that variant's section and also for a couple of others. I guess I could specifically highlight that somewhere if that is what many desire. I am purposefully not providing the average move-count. This is due to recent methods using HARCS program numbers as representative of what humans can do. This has misled some members of the community and slightly altered expectations. Additionally, even if I did try to provide an exact number, it is actually impossible for that number to be perfect. I will say that the average movecount of most variants of this method will be around the same as Roux. More advanced variants will average 3-4 moves fewer.
You could, however, say how many moves each of the algorithm steps takes on average without any risk of being misleading. This way people could compare each of the Nautilus variants against each other.
 

Athefre

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You could, however, say how many moves each of the algorithm steps takes on average without any risk of being misleading. This way people could compare each of the Nautilus variants against each other.
Yeah, I can do that. I actually recently calculated the average number of moves for some of the sets. So I'll just add them to the documents.
 

ObscureCuber

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Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!
I'd recommend just starting out with the EO,OcLL PLL or OLL PLL since they will be what you are probably most familiar with, and EO is only 11 algs!
 

Athefre

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A more detailed explanation of the Nautilus name. The blockbuilding looks like a 3D version of the Fibonacci golden rectangle. This golden rectangle is often used to describe things in nature. It is most often associated with the Nautilus where the golden rectangle is layered over a Nautilus shell to show how the spiral of the shell matches the pattern. On a 3x3, when using the Nautilus method, the same pattern is created. Below is an image of the bottom of the cube. In the first step you build a 1x2x3, then after that a 2x2x2, then there are the remaining pieces. Starting with the empty pieces and going clockwise, it creates the pattern 1, 1, 2, 3. The 1x2x3 would extend to 3x3x3 on the left, but is restricted because it is a 3x3x3 cube.

Nautilus Golden Rectangle.png

I think we could have methods for other puzzles based on the Nautilus 3x3 method. The shape and concept of Nautilus should work well and provide some of the same freedom, ergonomics, and look-ahead. Big cubes, cuboids, minxes (though strange ergonomics in this case), and so on. I have a big cube version of Nautilus but haven't really posted yet.
 

ObscureCuber

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A more detailed explanation of the Nautilus name. The blockbuilding looks like a 3D version of the Fibonacci golden rectangle. This golden rectangle is often used to describe things in nature. It is most often associated with the Nautilus where the golden rectangle is layered over a Nautilus shell to show how the spiral of the shell matches the pattern. On a 3x3, when using the Nautilus method, the same pattern is created. Below is an image of the bottom of the cube. In the first step you build a 1x2x3, then after that a 2x2x2, then there are the remaining pieces. Starting with the empty pieces and going clockwise, it creates the pattern 1, 1, 2, 3. The 1x2x3 would extend to 3x3x3 on the left, but is restricted because it is a 3x3x3 cube.

View attachment 15249

I think we could have methods for other puzzles based on the Nautilus 3x3 method. The shape and concept of Nautilus should work well and provide some of the same freedom, ergonomics, and look-ahead. Big cubes, cuboids, minxes (though strange ergonomics in this case), and so on. I have a big cube version of Nautilus but haven't really posted yet.
I could ~try~ to make a nautilus method for megaminx, will update you if I find how to lol
 

Athefre

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What I was thinking is that you have those five pieces on the bottom right of a front layer. That would provide the same kind of movement as in Nautilus. It would also mean several variants could be used to finish. However, the ergonomics of moving the puzzle in that way aren't perfect.
 

ObscureCuber

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What I was thinking is that you have those five pieces on the bottom right of a front layer. That would provide the same kind of movement as in Nautilus. It would also mean several variants could be used to finish. However, the ergonomics of moving the puzzle in that way aren't perfect.
another variant you could make is kinda the way petrus is done on mega, were you get to last side and do EO (y') RB
you could simularly get to last side+one pair, EO, rfs , LL
 

Athefre

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another variant you could make is kinda the way petrus is done on mega, were you get to last side and do EO (y') RB
you could simularly get to last side+one pair, EO, rfs , LL
Let me know what you figure out. It would be nice to have something good for Megaminx that isn't LS+LL.
 

ObscureCuber

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Let me know what you figure out. It would be nice to have something good for Megaminx that isn't LS+LL.
the really sucks things about mega is that anything that doesn't go to LS>LL is really bad because of how the puzzle functions, I was trying it out, and while you can solve something like an extention of block, EO, its not worth doing because of how mega works.
 
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