What?? Seriously

Four Chained Zeros (5 btm).

Two Chained Half Zeros (14 btm).

Per

Another version of triangles:

Quadruple Triangle (43 btm).

I guess this could be improved ,,,

Per

When making a snake on the petaminx I realized I never made one on the master kilominx. So I did:



Watch the video at
Youtube

enjoy!

To continue the tradition, here's the peta snake. Actually it's a snake twin. Unfortunately the contrast pink/violet is low, so I include a schematic too.



Or watch it on Youtube

Wow! Impressive

Nice! The snake pattern on the master kilominx ia whole lot easier than same on the gigaminx

Per

Allright, I simply re-use a few separate algs for edges and centers and these were not meant to be optimal.
Anyway, yours are very short and should be darn close to optimum: I could'nt find anything shorter

Simple patterns can further be obtained by scaling the first part of the algorithm of the Two Chained Half-Zeros:
(TL2 B2) (N3U2 TF2 N3U2 T3F2 N3U2 N3F2) (B2 TL2)

Two Wide Edges
(VU2 F2 VU2 T3F2 VU2 VF2)
Two Wide Edges (6 btm)

Two Opposed Bricks (1x2x4)
(TL2 F2) (VU2 F2 VU2 T3F2 VU2 VF2) (F2 TL2)
Two Opposed Bricks (1x2x4) (9 btm)

Quadruple Triangle
A shorter version could be found by re-working the setup of centers and modifying the alg of edges:
Centers:
(U2 VD VL2 F' L') (VU NL' VU' NL NU VL' NU' VL) (L F VL2 VD' U2)
Edges:
(U' D' F2 L) (N3F2 SR B' SR' M2F2 SR B SR' N3B2) (L' F2 D U)
Quadruple Triangle (32 btm)

Cheers

I improved the:

Double Hexagon 6x6x6 (36 btm).

Inspired by the edge cycles for Quadruple Triangle (conjugated).

Edge cycles for Double Hexagon (6x6x6) (19 btm).

I was too lazy to remove cube rotations

Per

Double Hexagon (6x6x6)
Notice that the algorithm of edges can be further improved by transforming the inner alg to remove cube rotations and forcing the inverse setup to terminate with an L move:
(L' R' U2 F') (N3D2 SB' U SB M2U2 SB' U' SB N3U2) (F U2 R L) (17 btm)

Double Hexagon (6x6x6) (33 btm)

Nice improvement!!

So I used the improved edge cycles and improved the following:

Fat Double Hexagon (38 btm).

Required block 3-cycles:
L- R- U2 F- VD2 SB- U SB WU2 SB- U- SB VU2 F U2 R L

Per

Slight improvement:

2 opposite bricks (1x2x4) (8 btm).

Per

2 easy patterns based on the following:

SR F- M2U2 F SU F- M2U2 F SU- SR-

1. 6 Sort of X¨s (6x6x6) (16 btm).

2. 6x (6x6x6 pure version) (18 btm).

Per

A combined version this time:

Quadruple Triangle and Double Hexagon (52 btm).

Per

Quadruple Triangle and Double Hexagon (version 2) (52 btm).

Note striking similarity with previous version. Only 10 turns differ (8 for the centers of hexagons, and 2 for the edges of hexagons)

Per

Unnamed Pattern1 (22 btm).

Unnamed Pattern2 (16 btm).

Unnamed Pattern3 (16 btm).

Many other 3-cycle combinations like these ones are also possible. Not all save many turns compared to their more trivial setups

Per

6 Xs
A 2-move reduction can be obtained by scaling up this 3x3x3 pure alg MF' [R MU2 R' L' MU2 L, SU] MF to a 6x6x6 cube:
M2F' [R M2U2 R' L' M2U2 L, SU] M2F

6 Xs (6x6x6) (16 btm)

Pattern 2 (16 btm)
(N3F2 N3R2 N3U2 R) [F' M2U2 F, U] (R' N3U2 N3R2 N3F2)

Pattern 3 (16 btm)
(N3B2 N3L2 N3D2 R) [F' M2U2 F, U] (R' N3D2 N3L2 N3B2)

Patterns 2 & 3 are those of 2 edge triangles for which 14-move solutions already exist, if S moves are used instead of slice moves in setup:
Pattern 2 (14 btm)
(SF' U2 F2) [SU', L' N3U2 L] (F2 U2 SF)
2 Edge Triangles (6x6x6) (14 btm)

Here are a few more (unoptimized) edge patterns:

4 Edge Triangles
(SF' U2 F2) [SU', L' ND2 N3U2 L] (F2 U2 SF)
4 Edge Triangles (6x6x6) (16 btm)

2 Edge Propellers
(SF' U2 F2) [SU', L' WU2 L] (F2 U2 SF)
2 Edge Propellers (6x6x6) (14 btm)

8 Triangles
(Obtained from previuosly posted M2F' [R M2U2 R' L' M2U2 L, SU] M2F)
NF' NB [R NU2 ND2 R' L' ND2 NU2 L, SU] NB' NF
8 Triangles (6x6x6) (22 btm)

Another fun version:

2 Rectangle Bladed Propellers 3-Cycles (14 btm).

Per

Hi!

I imroved the following:

Quadruple Triangle and Double Hexagon (version2) (48 btm).

Per

4 Fat Triangles (55 btm).

I did not try to optimize this ...

Per

Yet another version:

4 Fat Triangles and 2 Fat Hexagons (57 btm).

I hope this one turns out quite optimised ...

Is there any obvious triangle/hexagon combos we did not cover yet??

Per

Hi Per,

Algorithms of centers can be shortened by reworking the setup, mainly by using S moves.

Quadruple Triangle and Double Hexagon (version2)
Centers (before):
(SR VD' F2 T3D2 R2 VD') (VD NF VD' NF') (ND VF ND' VF') (NB' VU' NB VU) (VB' NU' VB NU) (VD R2 T3D2 F2 VD SR')

Centers (after):
(SR SU2) (VD NF VD' NF') (ND VF ND' VF') (NB' VU' NB VU) (VB' NU' VB NU) (SU2 SR')

Quadruple Triangle and Double Hexagon (version2) (42 btm)


4 Fat Triangles and 2 Fat Hexagons
Centers (before):
(SR VD' F2 T3D2 R2 VD') (ND V3F ND' V3F') (V3D NF V3D' NF') (N3D N3F N3D' N3F') (NB' V3U' NB V3U) (V3B' NU' V3B NU) (N3B' N3U' N3B N3U) (VD R2 T3D2 F2 VD SR')

Centers (after):
(SR SU2) (ND V3F ND' V3F') (V3D NF V3D' NF') (N3D N3F N3D' N3F') (NB' V3U' NB V3U) (V3B' NU' V3B NU) (N3B' N3U' N3B N3U) (SU2 SR')

4 Fat Triangles and 2 Fat Hexagons (50 btm)

I used the same "trick" as Glazik to improve the following:

Quadruple Triangles and Double Hexagon (version2) (42 btm).

Old habits with long setups die hard

Per

Y-Spectre (6x6x6) (29 btm),

and

Triangle Spectre (6x6x6) (31 btm).

I guess both could be optimized

Per

Here are a few improvements, obtained mainly by insertion + shift

Y-Spectre (6x6x6)
Insertion 1:
(M2R' N3U M2R N3U' N3L M2U NL NU NL' VU' NL VU VL' V3U')

Insertion 2:
(N3R' VD' N3R N3D NR' ND N3R' N3D' VR N3D)

Insertion 1 + 2:
(M2R' N3U M2R N3U' N3L M2U NL NU NL' VU') (N3D) (N3R' VD' N3R N3D NR' ND N3R' N3D' VR N3D) (N3D') (NL VU VL' V3U')

Setup:
(SF) (M2R' N3U M2R N3U' N3L M2U NL NU NL' V3U' N3R' VD' N3R N3D NR' ND N3R' N3D' VR NL VU VL' ND') (SF')
Y-Spectre (6x6x6) (25 btm)


Triangle Spectre (6x6x6)
Same as above but with setup modified:
(SR' SU) (M2R' N3U M2R N3U' N3L M2U NL NU NL' V3U' N3R' VD' N3R N3D NR' ND N3R' N3D' VR NL VU VL' ND') SF CU'
Triangle Spectre (6x6x6) (26 btm)


By composing 2 already published patterns, 6 large arrows can be displayed on a 6x6x6 cube (not optimized yet):
Centers:
R' L' MF MD MF' MB' MU' MB NF ND NF' NB' NU' NB WU L R

Corners:
(R' D2 R B' U2 B) (R' D2 R B' U2 B)

Edges:
(SF' U2 F2) [L' WU2 L, SU'] (F2 U2 SF)
6 Large Arrows (6x6x6) (41 btm)

Hi

I improved the first part to : NU NL NU- M2L N3U V3L- N3U- N3L V3U N3L- V3U-

So the improved version becomes: Y Spectre (6x6x6) (23 btm)

And another improved pattern:

Triangle Spectre (6x6x6) (23 btm).

Per

Yet another improvement:

6 Large Arrows (6x6x6) (33 btm).

Breakdown:

Corners and edges: F D2 B R B- L- F D- L2 F2 R F- R- F2 L- F-
Centers: R- L- MF MD MF- MB- MU- MB NF ND NF- NB- NU- NB WU L R (same as you Glazik)

Per

By working again on insertion + shift, a 2-move gain has been obtained.

Y-Spectre (6x6x6)
1- Replace (V3L N3U V3L' N3U') (N3L V3U N3L' V3U') with:
N3L V3U N3L' N3U' V3L N3U V3L' V3U'

2- Insert (NU NL NU' NL') to get:
N3L V3U N3L' N3U' V3L N3U M2R NU' NL' M2U'

3- Insert result at * into (N3R' VD' N3R N3D NR' * ND N3R' N3D' VR N3D):
(N3R' VD' N3R N3D NR') (N3L V3U N3L' N3U' V3L N3U M2R NU' NL' M2U') (ND N3R' N3D' VR N3D)

Y-Spectre (6x6x6) (21 btm)

Same process for the second pattern:
Triangle Spectre (6x6x6) (21 btm)

No shorter alg could be found for the '6 Large Arrows' pattern

But I found:

6 Large Arrows (6x6x6) (31 btm).

Per

Two additional (unoptimized) patterns:

6 Small Arrows
F (D2 B R B' L' F D' L2 F2 R F' R' F2 L') F'
SF' NU NR' NU' ND' NL ND NL' NR SF
6 Small Arrows (6x6x6) (26 btm)
By replacing centers with 'L-type' centers, rings may be obtained instead of arrows, although I haven't gone any further.

2 Triangles (4-4-4)
This is an improved version of Walter's algorithm.
(SF' U2 F2) (L' N3U2 L SU' L' N3U2 L SU) (F2 U2 SF)
(B' F' L2 U D) (N3F NU' N3F' NF N3U' NF' VU) (D' U' L2 F B)
2 Triangles (4-4-4) (6x6x6) (29 btm)

A few more (improvable) patterns:

6 Triangle Boomerangs
(WR WF' WR' WF)
F D2 R2 B (V3R' V3D' V3R V3D) B' R2 D2 F'
6 Triangle Boomerangs (6x6x6) (15 btm)

6 Y Boomerangs
(WR WF' WR' WF)
B' F' U2 L2 (V3R' V3D' V3R V3D) L2 U2 F B
6 Y Boomerangs (6x6x6) (15 btm)

6 Offset Rings
Centers:
(WR WF' WR' WF)
F D' R' B (V3R' V3D' V3R V3D) B' R D F'
Edges:
F (D2 B R B' L' F D' L2 F2 R F' R' F2 L') F'
6 Offset Rings (6x6x6) (28 btm)

I improved the:

6 Offset Rings (6x6x6) (25 btm).

and made a new contribution:

6 Offset Windows (6x6x6) (25 btm).

and finally:

6 Nested Offset Rings (6x6x6) (29 btm).

Per

Good optimization work, Per!

I guess the following one could be shortened too:

2 Y Loops
Centers:
(WR WF' WR' WF)
F B D2 R2 (V3L V3U V3L' V3U') R2 D2 B' F'
Edges:
SF R2 F2 SR D NR2 D' SR' D NR2 D' F2 R2 SF'
2 Y Loops (6x6x6) (27 btm)

Classic pattern on a 3x5x7 Cuboid:

Hi

I could not improve the 2Y Loops, but i made this variation instead:

2 Small Y Loops (6x6x6) (27 btm).

Smaller loops is also possible, will post that later

Per

How about an American flag pattern? Picture plus algorithm.

That would require the 17x17x17 cube

Per

Or maybe a 100x100x100 cube to be close to the 'G-spec'

The picture below shows a flag designed with the following values:
A = 52 px
B = 98 px
C = 28 px
D = 44 px

The algorithm is based on 3-cycles of centers (see demo 100x).

A few more loops...

2 Y Loops (4x4x4)
Centers:
(WR WF' WR' WF)
F B D2 R2 (ML MU ML' MU') R2 D2 B' F'
Edges:
SF R2 F2 SR D MR2 D' SR' D MR2 D' F2 R2 SF'
2 Y Loops (4x4x4) (27 btm)

2 Loops - Variation 1 (6x6x6)
Edges:
(SU' L2 D2 SR' F NL2 F' SR F NL2 F' D2 L2 SU)
Centers:
(U D R B2 L) (WR' WU WR WU') (M3U M3R' M3U' M3R) (L' B2 R' D' U')
2 Loops - Variation 1 (28 btm)

2 Loops - Variation 2 (6x6x6)
Edges:
(SU F2 U2 L NF2 L' SF L NF2 L' SF' U2 F2 SU')
Centers:
(U' D' F2 L' R') (WR' WU WR ND M3R' M3U' M3R) (R L F2 D U)
2 Loops - Variation 2 (28 btm)

Long time. No pattern, So here goes:

Double Y-loops (6x6x6) (39 btm):

Could still be optimised i guess

Breakdown:

Centers:
(F B R2 D2) WR- WU WR VD VL VU- VL- V3R- V3D- V3R ND M2R- M2D M2R (D2 R2 B- F-)

Edges:
SF R2 F2 SR D N3R2 D- SR- D VR2 D- SR D NR2 D- SR- F2 R2 SF-

Per

The algorithm of edges has been slightly improved (2 moves):
(SF' U2 F2 L') (N3U2 L SU' L' VU2 L SU L' NU2) (L F2 U2 SF)

2 Double Y-Loops (37 btm)

Still no other pattern in sight...

Long time, no new pattern contribution.

Here goes:

Zig-Zag (6x6x6) (22 btm).

I will post zig-zag for other sizes later. 3x3x3 is well known:

Zig-Zag (3x3x3) (12 btm).

And the 4x4x4 version:

Zig-Zag (4x4x4) (15 btm).

Note that this works also for AI bandaged 4x4x4, as it was originially developed for


Per

Hi Per,

The solution to the AI 4x bandaged cube uses a clever combination of T-moves and cube rotations

With a little help from Cube Explorer, solutions to the two other patterns have been slightly improved:
Corners:
CU2 U2 D' L2 F' L2 WU2 L2 F' L2 D'
Centers:
TD F2 TL2 NU ND' VL2 M2U N3L2 WU' L2 F2 T3D'
Zigzag (6x) (21 btm)

Corners + Edges:
D2 U' R2 F MU2 F2 MU2 F' R2 U'
Zigzag (3x) (10 btm)


These two may well be new:
2 Edge-Diamonds (3x) (8 btm)
4 Tees (5x) (14 btm)


Ideas for new patterns may also come up from symbols, letters or characters in other languages, especially from chinese (simplified) characters.
Here are a few fairly unoptimized algs of simple 5x patterns:
4 Wáng (emperor) patterns (5x) (9 btm)
4 Tǔ (ground) patterns (5x) (9 btm)
4 Shàng (above) patterns (5x) (15 btm)
4 Shān (mountain) patterns (5x) (14 btm)

Nice diamonds with good optimisation

I improved the 4 Tees (5x5x5) (10 btm),

Per

These 2 patterns have been improved since:
4 Shàng (above) patterns (5x) (11 btm)
4 Shān (mountain) patterns (5x) (12 btm)

Another interesting chinese symbol is the Bāguà (8 trigrams). Trigrams are simple patterns that can be displayed by 2 per cube (same middle line and opposed top and bottom lines, on adjacent faces):

Qián – Kǎn (5x) (10 btm)
Lí – Kūn (5x) (12 btm)
Duì – Xùn (5x) (11 btm)
Zhèn – Gèn (5x) (13 btm)

Hi!

I improved the
Zhèn - Gèn (5x) (8 btm).

And the
Li - Kùn (5X) (6 btm).

And the
Qián - Kàn (5X) (5 btm)

And finally the
Dui - Xún (5X) (6 btm).

You seem to be fond of chinese symbols

Per

Well, I'm taking a Mandarin class...

A very slight improvement:
Zhèn – Gèn (5x) (7 btm)

I guess the two following algs could be improved as well:

Diamonds:
Corners
WU2 R2 B' R2 WU2 R2 B' R2
Centers
R2 B2 NU' ND NB2 WU MF2 MU' T3B2 R2
2 Edge-Diamonds (5x) (15 btm)

Zigzag:
Corners
CU2 U2 D' L2 F' L2 WU2 L2 F' L2 D'
Centers
ND' F2 L2 WU MR2 MU' VL2 ND NU' TL2 F2 ND
Zigzag (5x) (21 btm)

Nice work as always Glazik

One more easy contribution:
6X (5X) (12 btm).

And the last zig-zag version:
Zig - Zag (7X) (24 btm).

For good measure:
6X (7X edition) (16 btm).

One or more of these could surely be optimised.

Per

A new variation:

4 solid Diamond Edges (7X) (12 btm).

And

4 solid Diamond Edges (5X) (8 btm).

This will obviously generalize to any odd size nxnxn cube and require (n-1)*2 turns

Two more:

Orthogonal mirrored T's (5X) (21 btm).

and

Orthogonal mirrored T's (7X) (30 btm).

Per

I tried to find shorter versions of your lastly published algs but found none. Good work as usual, Per.

Here are a few new patterns:
Edge-Diamonds (7x):
Corners
SF R2 F B L' F' B' R2 B F L F2
Centers
F2 L2 ND' NU V3L2 MU' MR2 M3U N3L2 VU' VD NL2 L2 F2
2 Edge-Diamonds (7x) (21 btm)

Bricks (4x):
Corners
SU2 L2 F' L2 SU2 R2 B' R2
Edges
L2 MF2 MU2 TF2 MU2 F2 MU2 L2
2 Bricks (1x1x4) (4x) (13 btm)

Bricks (6x):
Corners
SU2 L2 F' L2 SU2 R2 B' R2
Edges
L2 VF2 VU2 T3F2 VU2 F2 VU2 L2
2 Bricks (1x1x6) (6x) (13 btm)

4 I's (5x) (8 btm)

And finally, another well-known chinese symbol
This last one could certainly be shortened.
Notice that 2 additional patterns may also be added on faces R/L.
Square Yin-Yangs (6x):
Corners
WU2 L2 F' L2 WU2 L2 F' L2
Edges
L2 VF2 VU2 T3F2 VU2 F2 WU2 VL2 T3D2 VL2 D2 T3L2
Centers
VR2 VD2 NR2 ND2 N3R2 B2 ND2 N3R2 ND2 N3R2 B2 N3D2
2 Square Yin-Yangs (6x) (29 btm)