# User:GUYTU6J/Repeat

 This article contains many LifeViewer windows that may make the page slow.

Repeat is an unusual way to create exotic patterns. The idea was put forward in 2012[1], and was revisited in a discussion on the Replicator rule in 2016.[2]
In normal cellular automata investigations, the states of cells in a continuous evolution are altered solely according to the rule. But this is not the case here: a subpattern is repeatedly xor-pasted in during evolution. This gives insights into (pseudo-)superluminal effects in CAs. The following assumes regular Life (B3/S23) specifically.

## Key parameters & Implementation

There are three governing parameters, namely x-offset, y-offset and time-interval, that tell how to paste repeatedly. For instance, (5,-2,1) means to move 5 cells right, 2 cells up as well as to advance by 1 generation between successive pastes. Another parameter is the times to paste, but it is usually set to some large numbers (e.g.1000) in order to neglect edge effects.

Besides manual repeating, there have been two automatic ways to make a such pattern since early April, 2020. They depend on golly (equipped with python) and LifeViewer respectively.
With golly, create a new .py file and write in the following python script:[3]

import golly as g
s = g.getselrect()
if s == []:
s = g.getrect()
xy = [0, 0]
s = g.getcells(s)
if s == []:
g.exit("Pattern is empty.")
disp = g.getstring("Enter displacement in form (x,y,t):", "2,0,1").split(",")
n = 0
try:
disp = (int(disp[0]), int(disp[1]), int(disp[2]))
n = int(g.getstring("How many times to repeat?", "25"))
except:
g.exit("Invalid input.")
g.new("a")
g.putcells(s, xy[0], xy[1], 1, 0, 0, 1, "xor")
for i in range(n):
xy[0] += disp[0]
xy[1] += disp[1]
g.run(disp[2])
g.putcells(s, xy[0], xy[1], 1, 0, 0, 1, "xor")

When running the script, enter the parameters in the two dialogs.
With LifeViewer, use this code:[4]

x = 0, y = 0, rule = B3/S23
!
#C [[ PASTEMODE 6 PASTEDELTA <x-offset> <y-offset> PASTET EVERY <time-interval> 0 <times_to_paste> PASTE <rle> STOP <times_to_paste> ]]

For example, taking a glider and applying (5,-2,1)-pasting 25 times results in the fleet on the right (for clarity, marked in LifeHistory)

With LifeViewer: (extra commands for better visualization)

## 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 pattern on the right can be regarded as an almost spaceship with speed (2,0)c/1 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 just disintegrates without further repeating that supports it to go superluminally.

## General tructures

Similar to the crystals, patterns arising from repeat (provided enough iteration) possess various structures. Different parameters lead to very different appearance. Let's look at (2,0,1), which is used above. Applying it to a scribble:

Inside the intricate stuff one can spot certain motifs. There is a common wick:

From some portions agars can be extracted as well, for instance the upper corner.

A collection of extracted agars is on a separate page:User:GUYTU6J/Repeat/Appendix 1: agars from (2,0,1)

In the case of (2,1,1), half-pyramid shaped knightwise-travelling results are obtained. Note that the y-offset at 1 per generation matches the speed of superstrings.
For example, do (2,1,1) transformation to a block:

This time the pattern does not converge: the more time it is iterated, the more interesting it is.
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. To compare:

With other parameters of the form (x,1,1), where x > 2, superstrings arise frequently. They can be spaceship-like, such as this (4,1,1) pattern:

Or puffer-like, for instance this (5,1,1):

With (2,2,1), the block leads to an expanding zebra stripes agar.

As for a scribble...

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

## Notable 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. Stabilization with ordinary technology (spaceships, puffers, rakes, etc.) is yet to be found. 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)

## References

1. Jackk (May 20, 2012). 2c? If only? (discussion thread) at the ConwayLife.com forums
2. muzik (March 2, 2016). Replicator (discussion thread) at the ConwayLife.com forums
3. FractalFusion (March 7, 2016). Re: Replicator (discussion thread) at the ConwayLife.com forums
4. Chris Rowett (April 9, 2020). Re: Pattern viewer for forum threads (discussion thread) at the ConwayLife.com forums