The Octadecayotton ( Dimensions)

who'll be there when i'm gone?

Dimensions used: 3 Dimensions 4 Dimensions 5 Dimensions 6 Dimensions 7 Dimensions 8 Dimensions 9 Dimensions 10 Dimensions 11 Dimensions 12 Dimensions

By default 9 dimensions is used, but multiple Octadecayottons or mod settings can change it.

The spheres will start moving, resembling the rotations of a -dimensional cube. 3 rotations are shown, followed by a brief pause before starting over.

Identifying Dimensions

• There are dimensions: . Each axis can either be positive, or negative.
• Any positive axis points to the right (+X), up (+Z), and/or towards (+Y) the viewer when viewed from the front.
• Any negative axis points to the left (-X), down (-Z), and/or away (-Y) the viewer when viewed from the front.
• Any given sphere has neighbours, which are all 1 of each of the axes, either positively or negatively.

• To the diagram to the right shows on example of a sphere's neighbours as seen from the front. The unfilled spheres are neighbours of the filled sphere.
• In reading order (left-to-right then top-to-bottom), the spheres are .
• In this example, going from the filled sphere to any unfilled is a positive axis, while going from an unfilled sphere to the filled sphere is a negative axis.

Identifying Rotations

• Look at 2 spheres that are neighbours (note down their initial axis that connects them together) and watch them transform.
• If these 2 spheres are now neighboured from a different axis, that implies a rotation. Record the new axis that they transformed into, and repeat this process starting with the new axis until the first initial axis is reached.
• For any negative initial axis, invert both the initial and new axis. (positive -> negative, negative -> positive)

Identifying Rotations (...continued)

• When the first initial axis has been reached, start from the bottom of the list, and working your way up; append all the new axes to a separate list.
• The resulting list is called a subrotation. In a given rotation there can be multiple simulatenous subrotations happening at the same time.

Primary Values

• All rotations and subrotations have a primary value. Within each subrotation, create a list of every possible pair of axes from itself and the next axis. (including the last and first axis as a pair*)
• If the subrotation contains exactly 1 axis, ignore the above rule and make only 1 pair, consisting of the axis repeated twice.
• For each pair, get the value from the table, using the first letter as the row and the second letter as the column.
• If 1 of the 2 axes are negative, multiply the pair's result with -1.

^{* Even with 2 axes, this rule still applies. For example, subrotation +R-T gives +R-T and -T+R.}

		X	Y	Z	W	V	U	R	S	T	O	P	Q
X		1	2	5	1	8	8	1	5	2	1	2	5		X
Y		2	3	6	2	9	9	2	6	3	2	3	6		Y
Z		9	1	4	9	7	7	9	4	1	9	1	4		Z
W		1	2	5	1	8	8	1	5	2	1	2	5		W
V		2	3	6	2	9	9	2	6	3	2	3	6		V
U		9	1	4	9	7	7	9	4	1	9	1	4		U
R		1	2	5	1	8	8	1	5	2	1	2	5		R
S		2	3	6	2	9	9	2	6	3	2	3	6		S
T		9	1	4	9	7	7	9	4	1	9	1	4		T
O		1	2	5	1	8	8	1	5	2	1	2	5		O
P		2	3	6	2	9	9	2	6	3	2	3	6		P
Q		9	1	4	9	7	7	9	4	1	9	1	4		Q
		X	Y	Z	W	V	U	R	S	T	O	P	Q

Primary Values (...continued)

• The absolute sum of all pairs on all subrotations is the primary value of that rotation. Later in this manual, whenever p₁, p₂, or p₃ is mentioned, it refers to the primary value of the 1^st, 2^nd, and 3^rd rotation respectively.

The Anchor Sphere

• Create 4 codes, named a₀, a₁, a₂, and a₃, each starting with the value . a_1-3 represent rotations 1-3.
• Subtract the largest number equal or less than p₁ found in "Decimal <-> Binary" from it, then set a₁'s Xth digit from the left to 1, where X is the position obtained from that same number that was subtracted with. Keep subtracting and setting digits to 1 until p₁ is 0.
• Repeat the above step using p₂ and a₂, as well as p₃ and a₃.

Decimal <-> Binary
Subtract 2048 1024 512 256 128 64 32 16 8 4 2 1 Position 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th

• Look at a₁ and its rotation, for each axis, invert the number's position (0 -> 1, 1 -> 0) according to this the table below.
• Repeat this for a₂ and a₃, then set a₀ based on these 3 conditions:
• If the digit of a₁ is 1, of a₀ to 1.
• If the digit of a₂ is 1, of a₀ to 1.
• If the digit of a₃ is 1, of a₀ to 1.

Axis <-> Position
+Axis +X +Y +Z +W +V +U +R +S +T +O +P +Q -Axis -Q -P -O -T -S -R -U -V -W -Z -Y -X Position 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th

The Anchor Sphere (...continued)

a_1-3 is now gray code, convert each one to binary:

1. The first binary digit will match the first digit of the gray code.
2. The next digit is a 1 if the sum of the previous digit of the binary code and the current position's gray code is exactly 1. Otherwise it's 0.
3. Repeat step 2 until digits are obtained. This is the binary code.

• Starting from a₁, add the current a with the previous a, and then refer to the next a. Don't carry (1+1 ≠ 10) and replace 2's with 0's on each step.
• Replace every 0 with - and every 1 with +. This is now the anchor sequence. Whenever the anchor sphere is mentioned, it refers to the only 1 sphere that matches all positive/negative attributes of the anchor sequence's axes. The position of each character represents what axis they belong to, with the order being "".

Pausing

• Interact anywhere on the module to pause it. The rotations will stop, and a sound cue is played to indicate that it is ready to be interacted with.
• Each time the module is paused, a random sphere is chosen. This is called the starting sphere. The starting sphere is white.
• The goal is to get the starting sphere to be on the same location as the anchor sphere.

Navigation

• When the module is interacted with during the being 0-, an axis is queued. Each submission from 0- represents an axis, though order is random.
• need to be queued for a valid input. When the timer's , it will try submitting the . The queue is cleared if any other number of axes are queued.
• The starting sphere goes to the other side of all that were submitted.
• During this submission, all axes can only be submitted up to 2 times.
• When the starting sphere is in the same position as the anchor sphere, submit all axes. The module will strike or solve accordingly.
• Striking the module will unpause the module.