iLife - Optimal sequences
This page was kindly provided by Dr William Paulsen of Arkansas State University in Jan 2003, it is a follow up to his earlier findings described under the heading riding the glider. This page includes several optimal iLife sequences, including a sequence that builds a Light Weight Space Ship. Together these sequences provide the means of building glider guns much more efficiently than ever before. Knowledge of traditional Life terminology and glider-gun formation helps here, as does an understanding if the concept of iLife. For an introduction to iLife see the Maze of life V1 page.
The rest of this page is in Dr Paulsen's own words, click on any highlighted sequence to see a demonstration.
First of all, I wanted to see which life-forms can easily be spawned the way that the blinker and glider were spawned. I decided to examine all combinations that could be produced in 20 moves, starting from the loaf position, which seems to act as a gateway.
From a computer search I found there are 25466828 ways of traveling from the loaf position within 20 moves. Of these, 13730 have the blue cell riding a glider, sometimes with other debris that could potentially spawn a life-form. I then went through the 13730 pictures and worked out which of these produced anything interesting (this was the time consuming part!). My work was rewarded with the following results.
Forms a new glider using only 16 moves beating my 19 move record.
Forms a ship using only 19 moves. This is very useful in forming a glider gun, since before we had to build a ship by first spawning a blinker and hitting it with a glider.
Forms an eater using 20 moves, important for developing complicated life structures. This is the unique way of producing the eater in under 21 moves.
Forms a Light Weight Space Ship (LWSS) using 19 moves! This last example is the unique way of producing the LWSS in under 21 moves. It also provides a powerful tool as seen below.
Having the ability to launch LWSS as well as gliders is like having both rooks and bishops in chess: they can be used together to form complicated structures very quickly. To demonstrate, here is a sequence that produces a glider gun in only 247 moves (starting from the EEN loaf):
|L/R>LS>\\><<DS<<U/<||Builds a formation that eventually becomes a bi-block|
|<R\LSSSLS>></\D\||Spawns a block|
|R\LSD\><LSS\SLSUR\>||Spawns a ship|
|R<LSU</\LSS<SLSDR</||Spawns another ship|
|D\U/D>SD/\/<\||Spawns another block|
|L>RSU>SR/DDDLS<<U\S||Launch the LWSS! This eventually hits the bi-block which becomes a glider aimed back toward the ship|
|L/SUSU<<U<D>>>/RS<R>||Creates a formation which is a pure glider generator. That is, it produces a glider with no debris after 63 moves. I call this a fused glider since it gives the blue cell time to produce a second, or even a third, glider which forms simultaneously. In this case it merely allows the completion of the glider gun early.|
It is interesting that the LWSS needs to run into a bi-block to form a single glider going in the other direction. Ironically, I came very close to throwing out the "pseudo-life" formed during my exhaustive search, but decided to leave them in.
Dr William Paulsen - January 2003
material - Dr William Paulsen 2001-2002
applet - © Andrea Gilbert 2000-2002
applet JS conversion - cheerpj transpiler from Leaning Technologies - 2020