On the Subject of Kugelblitz

S u c c u m b t h e v o i d

This module will display a dark orb with seven coloured particles spinning around it rapidly. The particles are either coloured (1) or greyscale (0). Every solve alternates the greyscale between black and white. For each solve take the binary values of all the particles in rainbow order (ROYGBIV). If a colour does not appear, that bit is a 0, as it is a greyscale particle. XOR this binary string with the previous (if possible) to obtain your new binary string. For multiple Kugelblitz modules, refer to their colours in this manual. The final value is your starting coordinate formulated as Rxxxyyy, with xxx and yyy being the binary equivalent of X and Y with (X, Y) = (0, 0) being top left.

When this module is ready to be solved, the particles will slow down drastically and turn either white, or a pure rainbow colour. They will also pulse black every 2.5 seconds. Starting with north go clockwise 45 degrees for each coloured particle on the module to obtain your initial direction.

Iterating a Kugelblitz

Use the process below to obtain your numbers. The table (found on the second page) is wrap-around like a klein bottle: wrapping around north and south flips the table around the vertical axis and wrapping around east and west flips the table around the horizontal axis. Stop when you obtain 7 digits.

1. Start at the starting coordinate facing in the starting direction on the table. n is initially 0.
2. Add the value of the position you are on to the current value and go forward in your direction one step.
3. Repeat previous process another n times.
4. Modulo the resulting value by 7 to obtain a digit.
5. Rotate 135 degrees counterclockwise if you had R = 1 and 135 degrees clockwise otherwise.
6. Set your value back to 0, add 1 to n and return to step 2.

Convert each digit individually to 3-bit binary, keeping 0's. Prepend this binary sequence with a 1.

For each bit, 1 becomes an 'i' and '0' becomes a 'p', with a few exceptions: If there are already three 'i' in a row, the next character is always a 'p'. If there are already two 'p' in a row the next character is always an 'i'. If the amount of 'i' before a 'p' is even, the character after the 'p' is an 'i'. Convert the bits from left to right.

If there is an odd amount of occurrences of the letter 'i' in your sequence, append an 'i' directly to the end of the sequence.

For every 'p', wait a pulse and for every 'i', toggle between holding and not holding the orb while staying within that pulse.

If this has been done correctly, the orb will decay. On a strike, the module will display the binary sequence of one stage earlier, so when missing a stage it is advised to strike at that moment to get the binary for the missed stage.

5	1	3	6	4	0	2
1	2	6	4	0	5	3
4	0	5	1	3	2	6
3	5	2	0	1	6	4
0	3	4	2	6	1	5
6	4	0	5	2	3	1
2	6	1	3	5	4	0

Coloured Kugelblitz

General information

A coloured Kugelblitz will not create its own sequence, but rather affect how the sequence of the normal Kugelblitz (there will always be one normal Kugelblitz) is obtained.

Just like a normal Kugelblitz, the module will display a binary sequence in rainbow order, however the colour of the coloured Kugelblitz has been swapped with black, meaning that a black particle returns a 1 for the bit its colour is responsible for. Note that you do not always have to XOR the binary sequences.

The final sequence can be inputted on any Kugelblitz and it will solve all of them simultaneously. Striking on a Kugelblitz will also go to the previous stage on the other Kugelblitz modules.

Quirks

Red

Take the sum of all the n'th bits of the binary sequences, modulo 7 to obtain the n'th digit of the digit string. Add these values to the n'th digit of the normal Kugelblitz' final values before the binary conversion, modulo'ing by 7 in the process.

Orange

XOR the binary sequences. If the n'th digit is a 1, invert the n'th triplet (or quadruplet if combined with yellow), disregarding the prepended 1.

Yellow

XOR the binary sequences. Prepend the n'th triplet with the n'th digit of this sequence, disregarding the prepended 1 at the beginning of the binary string.

Green

Take the sum of all the n'th bits of the binary sequences, modulo 7 to obtain the n'th digit of the digit string. Add these values to the n (index starting at 1) modulo'ing by 7 in the process. Replace any 0's with 7's. This will be the amount of times you move forward within the n'th step, instead of using the standard 1234567.

Blue

Take the sum of all the n'th bits of the binary sequence, modulo 3 to obtain the n'th digit of the digit string. Add the fifth (blue) digit to the other digits, modulo'ing by 3 in the process. Replace any 0 by a 3 and remove the fifth (blue) digit from the sequence to get your 6-digit sequence. For each of the rotations you make, use the corresponding digit, where 1 means a rotation of 45 degrees, 2 a rotation of 90 degrees and 3 a rotation of 135 degrees, instead of using the standard sequence 333333 and rotating 135 degrees each time.

Indigo

XOR the binary sequences. XOR each digit with the sixth (indigo) bit. Remove the sixth (indigo) bit from the sequence. For each of the rotations you make, use the corresponding digit, where 1 means changing from clockwise to counterclockwise and vice versa and 0 means you do nothing. Do this swap before executing the rotation.

Violet

Split up the binary sequences in whether they were obtained on an even or an odd stage. Take the sum of all the n'th bits of the binary sequences, keeping this split in mind, modulo 7 to obtain the n'th digit of the digit string. The group containing the first stage will be laid out horizontally and then duplicated to get 7 rows of this sequence. The other sequence will be laid out vertically and then duplicated to get 7 columns of this sequence. Add up each position of these 7×7 grids together with the 7×7 grid in the manual, modulo'ing by 7 in the process. Use this new grid instead of the grid in the manual.

White

This type of Kugelblitz will only appear if every other colour was not available anymore. This module will not do anything and will automatically solve when the other Kugelblitz modules solve.