# User:GUYTU6J/Repeating recreation

Let's have fun with the "repeat" script! It can be found here (python) and basically transforms a given pattern to another via repeated xor-pasting, hence the name.
The script uses three parameters, (x,y,t). They are for x-displacement, y-displacement and generation-offset respectively. The script asks for another parameter which defines how many times to paste. This parameter is usually set to some large numbers (e.g.1000) in order to investigate ignoring edgy defects.
For instance, (5,-2,1) means to move 5 cells right, 2 cells up as well as advance by 1 generation between successive pastes. Doing this 25 times will transform the glider on the left into a stream of 26(indeed, not 25) gliders on the right (for clarity, marked in LifeHistory)

Alright, time for fun! The following summary assumes B3/S23 specifically; other rules can be investigated similarly.

## Superluminal moving partials

The first thing to notice is that repeaing yields patterns looking like partials of spaceships or puffers/rakes. Generated from a block and (2,0,1) transformation, the following pattern can be regarded as an almost (2,0)c/1 spaceship that is only 4 cells off:

Thanks to the superluminal property, the partials can self-repair at the back no matter how complicated they are, since the impact of chaos travels no faster than lightspeed, for example:

The front end obviously just disintegrates without further repeating that supports it to go superluminally.

## Structures

The aforementioned "partials" possesses various structures. For instance,structures arising from (2,0,1) include simple zebra stripes:

and reciprocating agars:(seed on the right)

and even more:

Extracting agars is possible, but their repeating unit can be large:

With other parameters of the form (x,0,1) where x > 2, the results are less interesting.

In the case of (2,1,1), the behavior can be quite interesting, since the y-displacement at 1 per generation matches the speed of superstrings.
For example, do (2,1,1) transformation to a block and some half-pyramid shaped knightwise stuff will arise on the right:

It is full of interleaved zebra stripes, simple superstrings and seemingly random chaos.
The lower part portraits a superstring with complex structure at the back, which tends to be periodic at x-direction. The periodic part can be put into a cylinder:

This is a dirty puffer yet to be stabilized. However, its stabilization involves mechanism similar to aforementioned self-repairing, leading to elongation of stabilized region that goes knightwise - to see this, compare its generation 0 with generation ~4000, when it expands to approximately twice of its initial length.
With other parameters of the form (x,1,1), where x > 2, superstrings arise frequently. Take this (4,1,1) pattern as an example:

With (2,2,1), the block becomes something like

For a general outcome of (2,2,1), see here.

Other parameters results in less complex structures, except the following...

## Obtaining waves

When applied certain transformations to some common evolution sequences (e.g. pi-heptomino, R-pentomino, lumps of muck...), waves (or less probably, wicks) occur. Measuring their velocity require specified direction, since such waves have low mods and both period and displacement are ambiguous. Examples:

(5,4,1) done to a t-tetromino
(click above to open LifeViewer)
(20,1,1) done to a stairstep hexomino
(click above to open LifeViewer)
(8,1,1) done to a R-pentomino
(click above to open LifeViewer)
(8,1,1) done to a honeyfarm predecessor
(click above to open LifeViewer)
(7,5,1) done to a honeyfarm predecessor
(click above to open LifeViewer)
(11,2,1) done to a honeyfarm predecessor
(click above to open LifeViewer)
(6,2,1) done to a pi-heptomino descendant
(click above to open LifeViewer)
(7,2,1) done to a pi-heptomino
(click above to open LifeViewer)