I found an alternative, quite short algorithm which can be scaled:

5x: Sparse Grids (Order 2)
NU2 NF2 NR2 NL2 NB2 ND2 (6 btm)

7x: Sparse Grids (Order 2)
VU2 VF2 VR2 VL2 VB2 VD2 (6 btm)

New pattern:

7X: U/D Layer Wide Grids (8 btm).

The equivalent 5X version is trivial by "downscaling"

And another quite easy one:

7X: Big Lantern (8 btm).

Per

7X: 6 Small Chessboard Faces (20 btm).

I'm sure this one can be improved somehow

7X: Jigsaw Edges (Order 2) (18 btm).

7X: Jigsaw Edges (Order2) v2 (19 btm).

Per

I just found a solution to create a cube in a cube like pattern:

5x: 4x4x4 Cube in a Checkered Cube
SF D2 F2 (L' NU2 ND2 L SD' L' NU2 ND2 L SD) F2 D2 B
L F U' R U F2 L2 U' L' B D' B' L2 U (30 btm)


Only little changes are required to achieve a 7x7x7 version:

7x: 6x6x6 Cube in a Checkered Cube
SF D2 F2 (L' NU2 MD2 ND2 L SD' L' NU2 MD2 ND2 L SD) F2 D2 B
L F U' R U F2 L2 U' L' B D' B' L2 U (32 btm)

The same pattern with a smaller cube in a cube:

5x: 3x3x3 Cube in a Checkered Cube
U B D R ((MD2 NR2)2 B MD2 B' MD2) R' D' B' U'
U B2 L U2 D' WF U2 D WF' L' B2 U'
TD TB TD2 TB' TU TL' TD2 TR TB' TU2 TF TD' TR TU2 TR' TU'
SF' U2 F2 (SU' L' NU2 L SU L' NU2 L) F2 U2 SF (58 btm or 55 btm actually)


... and on a 7x7x7:

7x: 5x5x5 Cube in a Checkered Cube
R U' L B2 D' N3R' VL N3U N3D' NL' N3U' N3D ND' N3R N3L' TD B2 L' U R'
TF2 TR2 TU2 TF' TD2 TB (TL TU')3 TB' TD2 TF'
SF' R2 B2 (U' NR2 MR2 NL2 U SR' U' NR2 MR2 NL2 U SR) B2 R2 SF
SF' U2 F2 (SD L' NU2 L SD' L' NU2 L) F2 U2 SF (67 btm or 65 btm actually)

7x: 4x4x4 Cube in a Checkered Cube
R U' L B2 D' (V3L VR' ND' N3R NU MD' N3L' NU' V3D N3D2 MR NR N3U NL' N3U' N3D) D B2 L' U R'
T3F2 T3R2 T3U2 T3F' T3D2 T3B (T3L T3U')3 T3B' T3D2 T3F'
SF' R2 B2 (U' NR2 MR2 NL2 U SR' U' NR2 MR2 NL2 U SR) B2 R2 SF
SF' U2 F2 (SD L' NU2 L SD' L' NU2 L) F2 U2 SF (73 btm or 71 btm actually)

Nice patterns Walter

I improved some of my own patterns:

7X: Jigsaw Edges (Order 2) (16 btm).

7X: Jigsaw Esges (Order 2) v2 (15 btm).

7X: 6 Small Chessboard Faces (18 btm).

Per

A new version

5X: Wide Rings in Checkered Cube (30 btm).

Number of versions on this theme seem almost countless; snakes, anacondas ...

Per

I tried to improve your Jigsaw Edges v2, but found a solution with the same length instead:

7x: Jigsaw Edges (Order 2) v2
N3L' N3R WD2 N3L' N3R N3B' N3F N3U' N3D WF2 N3U' N3D WR2 N3B' N3F (15 btm)


By removing the middle edges you get something very similar to Jigsaw Edges v1:

7x: Jigsaw Edges (Order 2) v3
M3R WD2 M3R M3F M3D WF2 M3D WR2 M3F (9 btm)

I improved one of the cube in cube patterns:

5x: 3x3x3 Cube in a Checkered Cube
SF U2 B2 (SD' R WD2 R' SD R WD2 R') (SD' R MD2 R' SD R MD2 R') B2 U2 SF'
SF' U2 F2 (SU' L' NU2 L SU L' NU2 L) F2 U2 SF
TD TB TD2 TB' TU TL' TD2 TR TB' TU2 TF TD' TR TU2 TR' TU' (52 btm or 51 btm actually)

Cool! This pattern epitomises what "patternising" is all about. EPIC! Maybe my alltime favourite Hope i can improve it some day

Per

Heh!!

I replaced

SF- U2 F2 (SU- L- NU2 L SU L- NU2 L) F2 U2 SF

with

SF R2 F2 (D NR2 D- SR D NR2 D- SR-) F2 R2 SF-

to gain 1 turn:

5X: 3x3x3 Cube in a Checkered Cube.

Now i'm sure even better can be found!

Per

Well, its a striking pattern indeed!
... and you can even put your favourite 3x3x3 patterns on it too.

For example:
5x: 3x3x3 Cube with 6 Dots in a Checkered Cube
TD' R U2 ND NB U2 NR2 U2 NB' U2 ND' R' ND NR2 D
SF U2 B2 (SD' R WD2 R' SD R WD2 R') (SD' R MD2 R' SD R MD2 R') B2 U2 SF'
SF R2 F2 (D NR2 D' SR D NR2 D' SR') F2 R2 SF'
TD TB TD2 TB' TU TL' TD2 TR TB' TU2 TF TD' TR TU2 TR' TU' (67 btm or 65 btm actually)

Very nice patterns from Per and Walter!

Here is my pretty small contribution

After Double Insertion:
SU R2 D2 (SR SF SR B WR2 SF NL2 F' SR' F NL2 SF' WR2 MR2 F' SR' F MR2 F') D2 R2 SU'
TL TD TL2 TD' TR TB' TL2 TF TD' TR2 TU TL' TF TR2 TF' TR'

5x: 3x3x3 Cube in a Checkered Cube (41 btm)

5x: 3x3x3 Cube with 6 Dots in a Checkered Cube (55 btm)

Wow, that's a major contribution, it saves up to 10 moves!
Excellent work!

Alternative solution;

7X: 6 Xs (Order 2) (21 btm).

Was hoping for even better after many insertions. Maybe later ...

Per

Here is another approach which also requires 21 moves.
But maybe it is possible to further improve it by insertions:

7x: 6 X (Order 2)
MR' N3U2 N3D2 MR'
MD' N3F2 N3B2 MD'
MF N3R2 N3L2 MF
M3R WD2 M3R M3F M3D WF2 M3D WR2 M3F (21 btm)

1 move gained by shifting Part 1:
MF MR N3U2 N3D2 MR MU N3F2 N3B2 MU MF N3R2 N3L2
M3R WU2 M3R M3U WF2 M3U M3F WR2 M3F
7x: 6 X (Order 2) (20 btm)

Another turned has been gained:

7X: 6 X (Order2) (19 btm).

This should be hard to beat. Much work has gone into this

Per

First attempt at new contribution:

5X: Rings in Checkered Cube (Order 3) (50 btm).

This can be improved for sure

2 turns gained by insertion:

5X: Rings in Checkered Cube (Order 3) (48 btm).

Per

3 more turns gained.

Insert (R2 U2) [SR, B NL2 NR2 B'] (U2 R2) at *:
NL NR' NU ND' NL' NR * NU' ND

Compose:
WR2 B U2 L WU2 F WR' F' WU L' U2 B' WR2 MR2
NL NR' NU ND' NL' NR R2 U2 SR B NL2 NR2 B' SR' B NL2 NR2 B' U2 R2 NU' ND
TD' TF2 TL' MF TU' MR' TU MF2 TL TF2 TD MR2

5x: Rings in Checkered Cube (Order 3) (45 btm)

Yet another contribution:

7X: 6 Hashtags (Order 2) v2 (27 btm).

Once again i believe it's not optimised. Through clever insertions better should be found

Per

1 turn gained again..

Transform 'S' to 'W' in Part 1:
WR' WU' N3D2 WF2 N3D2 N3L' WU2 N3L2 WF2 N3L' WU' WR

Shift Part 2:
V3R2 NL2 NB2 MF2 NF2 N3R2 N3U NL2 MR2 NR2 N3U2 NB2 MF2 NF2 N3U

7x: 6 Hashtags (Order 2) v2 (26 btm)

Beat you Glazik

1. SF SR (N3D N3F2 WR2 N3F2 N3D- N3U- WR2 N3U) SR- SF- (bars)

2. N3D- N3R2 NF2 MF2 NB2 N3R2 N3D N3U NF2 MF2 NB2 N3U- (dots)

7X: 6 Hashtags (Order 2) v2 (24 btm).

Did not find any way to do insertion ...

Per

New pattern again:

7X: Dotted Sparse Triple Cube (27 btm).

Composition is "obvious":

1. NF2 NR2 NL2 NF2 NU ND- NR2 NL2 NU- ND (prepare the dots)

2. T3F- T3U- MF- MR2 T3D- T3R T3U2 T3R- T3D MF- T3D- T3B T3R2 T3F- MU2 T3R2 T3B CF2 (sparse triple cube)

Similarly many other striking patterns can be made

Per

A little bit more esoteric:

7X: Striped Sparse Triple Cube (39 btm).

Per

Here is a number of simple (unoptimized) patterns based on variations of your last solution to the Hashtag algorithm:
ND NF2 MR2 NF2 ND' NU' MR2 NU

7x: Centers - Variation 1 (16 btm)

7x: Centers - Variation 2 (16 btm)

7x: Centers - Variation 3 (18 btm)

7x: Centers - Variation 4 (27 btm)

7x: Centers - Variation 5 (27 btm)

Nice vatiations Glazik. They all seem quite or completely optimised already

I improved my previous contribution by inserting last 3 turns appropriately:

7X: Striped Sparse Triple Cube (37 btm).

2 turns gained this way

Per

A big improvement:

7X: 8 Corner Loops (Order 2) (10 btm.

And a new version:

7X: 8 Big Corner Loops (Order 2) (10 btm).

Per

I suddenly realised i could add 3 easy turns to my Yahtzee pattern:

7X: 14 Small Loops (13 btm).

This reduces Glazik's 25 turn solution by almost 50 %

Per

Yet another cool pattern:

7X: 6 Linked Loops (Order 2).

I already optimised this one

Per

Hi Per,
Good work on optimizing algorithms!

Here are a few additional patterns, mainly rings:

7x: 2 Small Rings (6 btm)

I haven't found a 6-btm version for this one (to be optimized further?):
7x: 2 Large Rings (7 btm)

5x: 4 Wide Loops (6 btm)

7x: 4 Wide Loops (6 btm)

This last one might be used as a building block for 'true' 6 4-Cycles:
7x: Edge 6 4-Cycles (17 btm)

This would be my last contibution till February...

One easy improvement:

7X: 2 Large Rings (6 btm).

Start with 4 turn long bars and insert 4 turn short bars ...

Per

Small gain:

7X: Edge 6 4-cycles (16 btm).

(2 parts with 2 cancelling turns )

If my interpretation of "true" edges is correct it would be impossible. Ignoring
centers it could be done though
Per

Algorithm [N3R N3L', SF SR' SF'][SF SU2 SF', N3U] is a 'pure' Edge 6 4-cycles, ie. with no centers twisted.
This can be checked by using a supercube texture in CubeTwister, such as 7x: Orbit Cube.

We may wonder if a shorter solution may exist by allowing some centers to be twisted.

I think some interesting 2-color patterns per face could be obtained from this by connecting opposed edges with lines or dots...

A bit of confusion here. You can already see (by none side or corner permutations) that your algorithm and my algorithm are pure. I was thinking more like filling in the gaps between those edges. This would actually give 3 edge-block 4-cycles. But it would be impossible.

By twisted center i guess you actually mean permuted. Only the 6 extreme centers can be twisted

Per

Yet another simple contribution:

7X: 2 Long Gripping Loops (10 btm).

Per

Here is what i believe would be the shortest possible non-trivial 6 edge 4-cycles on the 7X:

7X: 6 Edge 4-Cycles (with centers side effect) (9 btm).

Composition:

1. [NR NL- , SF]

2. [NF- , SU2]

1 turn cancels for good measure. Only 3 turns from theoretical minimum (1 turn for each of the 3-cycles)

I could not improve the 16 turns with "invisible" center permutation.

Per

Easy pattern:

Circled and Scattered Dots (Order 2) (16 btm).

Per

Now a cool "trick":

This is 6 4-cycles on a 7x7x7 cube with no center side effects done in only 14 turns. The trick is that 4 of the cycles are disguised as 2 block cycles. However, looking at the edge permutations it's definitely 4 distinct 4-cycles also

7X: 6 Pure Edge 4-cycles (14 btm).

Per

Now it's my turn to post here I've got lots of patterns to show you!

3x3x2 cuboid-in-a-cuboid:


Square-2 umbrella:


Axis Cube checkerboard (colors only):


Mastermorphix checkerboard:


Pyraminx swirl:


Master Pyraminx checkerboard:


Megaminx Mezon:


6-color Skewb Ultimate superflip:

Great Ben!

How many turns to set up that first pattern for the 3x3x2 cuboid?? What was your approach?

Per

My approach:
1) Moving the block 2Ñ…2 from the bottom side on top;
2) 3-cycle of blocks 2Ñ…1;
3) J-permutation.
Algorithm: D2 B2 U B2 D' B2 F2 L2 U' L2 U L2 D' L2 U L2 U - [17]

My approach was to move the block of pieces from the bottom to the top layer (2 moves), resolve the top layer (10 moves) permute last layer corners (10 moves) and finally solve a 3-cycle of edges (16 moves). Not the most efficient method by far, but it's pretty easy to visualize.

And mine is :U- R2 U- R2 U2 F2 U- R2 U2 R2 F2 U- F2 U-

Done on 3x3x3 using insertion and disregarding middle layer!

Per

Well, here is something similar for the 4x4x4:

4x: 2 Cuboids (3x3x1) in a Cube
MF2 SR2 F' MB2 D' F L2 B' U ML2 MF2 TL2 MF2 L2 B' MF2 U' B2 R2 (19 btm)

Other patterns for the 4x4x4:

4x: Checkered Cube in a Cube
F2 L2 D F' B2 (MB2 R2)2 MR2 MB2 MR2 U' R B2 R' WD R WF2 R' D R
SR' ((MF MD MF') (MB' MU' MB) WD') L'
D2 R B' U2 B R' D2 R B' U2 B
SF' U2 F2 (L' MU2 L SU' L' MU2 L SU) F2 U2 SF (56 btm or 55 btm actually)

4x: Checkered Cube in a Cube v2
F2 R2 U' F' U R' U2 R U' F' MF2 R2 MF2 TR2 MF2 MR2
SR' ((MF MD MF') (MB' MU' MB) WD') L'
D2 R B' U2 B R' D2 R B' U2 B
SF' U2 F2 (L' MU2 L SU' L' MU2 L SU) F2 U2 SF (50 btm)

@ Walter:

The 2 checkered cube in cube patterns are the same, the only difference being physical rotation of the puzzle

My improvement (so far) is:

4X: Checkered Cube in Cube (41 btm).

I guess better would still exist (by insertion perhaps?)

Per

Of course, it's the same pattern. It's just a rotatet version.

By following the same approach I came up with a slightly shorter algorithm:

4x: Checkered Cube in a Cube
F2 R2 U' F' U R' U2 R U' F' MF2 R2 MF2 TR2 MF2 MR2
SF' (WD' (ML MD ML') (MR' MU' MR)) SF
SF L2 B2 (SR U' MR2 U SR' U' MR2 U) B2 L2 SF' (39 btm or 38 btm actually)

Minor improvement:

4X: Checkered Cube in a Cube (37 btm).

I simply replaced

SF' (WD' (ML MD ML') (MR' MU' MR)) SF

with

SF(WD' (ML MD ML') (MR' MU' MR)) SF'

Per

New contribution (easy variation):

4X: Fat Checkered Rings (33 btm).

Per