On the Subject of The Octadecayotton

"What could possibly go wrong?" - You, right now.

The module's appearance is initially blank.

Select the module, which causes the module to transform, spawning spheres in a rapid fashion. Face and embrace the void, it will only hurt a little.

The Octadecayotton ( Dimensions)

who'll be there when i'm gone?

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 1st, 2nd, and 3rd rotation respectively.

The Anchor Sphere

  • Create 4 codes, named a0, a1, a2, and a3, each starting with the value . a1-3 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)

a1-3 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.