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[Jan 2005: This article is now pretty badly out of date. More information... ]

17c/45 Spaceship, Part 1

By Jason Summers, Mar. 2003.

In this document, I offer moderately-detailed instructions for constructing the first ever 17c/45 spaceship in Conway's Game of Life. As of this writing, ten different velocities of spaceships are known; this would be the eleventh. The completed spaceship would be very large, by far the largest Life object ever constructed (perhaps somewhere around 50 million cells). Nevertheless, it is my hope that someone will eventually construct such a spaceship. If you are interested in doing any work on this, I'd appreciate hearing from you.

Most of the new Life patterns and technology described here were found by Jason Summers, David Bell, or Gabriel Nivasch.

Terminology used in this document:

blinker trail or trail
A single row of blinkers, 17 cells apart, with adjacent blinkers in opposite phases.
blinker track or track
A set of parallel blinker trails, upon which can travel one or more kinds of components built from pi's.
component
Usually used to mean a set of pi's, traveling in parallel on a set of blinker trails, that does something useful.
pi
A pi-heptomino object supported by a blinker trail.
pi's
Plural of pi. Probably spelled wrong.
rake
A component that periodically emits a glider or a spaceship.
separation
Usually used to mean the distance, in cells, between two blinker trails.
spaceship
A standard lightweight spaceship (LWSS), middleweight spaceship (MWSS), or heavyweight spaceship (HWSS).
Spaceship
When capitalized, means the 17c/45 spaceship that we are trying to build.

The key to building a 17c/45 Spaceship is the following well-known reaction. A form of the "pi heptomino" object (bottom), collides with a blinker (top-center, in red). The blue blinkers are only for reference, and are not part of the reaction.
generation 0

Advance the clock 45 generations, and this is the result:
generation 45

A new pi heptomino has appeared at the top, 17 cells above the original one. A new blinker, meanwhile, appears 6 cells below the original one, in the opposite phase relative to the reference blinkers. All the other cells will soon disappear, leaving only the same two objects we started with: a pi and a blinker.

So what can we do with this? First of all, note that a pi can climb a whole row of blinkers, spaced 17 cells apart:

This idea was used years ago by Dean Hickerson to build this "back and forth fuse" pattern (a p1200 oscillator), which appears in some Life pattern collections as "revfuse":

Or we can even use a puffer to build an infinitely long trail of blinkers:

But, while somewhat interesting, this doesn't necessarily lead anywhere. If only we could somehow move the blinker to the necessary position in front of the pi, without using any external objects that don't move at 17c/45, we would have a brand new spaceship. However, if you actually try to figure out how to do this, you'll soon conclude that it is next to impossible. And it is next to impossible... but don't let that stop you.

The next thing to notice is that the pi throws off a lot of sparks that aren't necessary to its survival, and that we could try to make use of for some other purpose. We can put two pi's side by side so that the sparks interact and do interesting things.

Most importantly, as David Bell was the first to discover, the sparks can interact and form a glider. For example:

I'll call an object like this a "rake", though that's not quite the usual meaning of the term. The numerals ("32") between the blinker trails in this and some other diagrams are only there to indicate the distance between the blinker trails.

It is important that a glider can slip safely between the blinkers. If it couldn't, we'd be pretty much stuck.

Several other backward rakes are known, and are shown in the appendix. [Note: In the interest of simplicity, the example patterns in this document use only the backward rake with separation 32. It may be advantageous to mostly use a separation of 30 instead, since there are two different rakes with separation 30. However, 30 is a little more difficult to construct, and note that the left halves of the two p30 rakes are identical, so the advantage may not be that much anyway.]

Every pi that climbs along a blinker trail shifts the blinkers by a certain amount. After 34 pi's have climbed the same trail, the blinkers will be restored to their original position and phase, and in the process they have cycled through every possible position and phase. This is important for maximum flexibility -- though it's too bad the trail is made of p2 oscillators (blinkers) instead of still lifes, requiring us to worry about their phase.

Only one forward rake is known that uses just two trails. It was found by Gabriel Nivasch after a long search, and has a separation of 32 cells. It is important that the separation is the same as that of one of the backward rakes.

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