Of course, there are tons of patterns large and small available online that are just a click away, so you sort of have to imagine yourself with a time machine to get the most benefit. You step out of your device sometime in the 70s or 80s to find a Life enthusiast busy with whatever program they use (and very likely wrote themselves).

"I am a future human," you intone, "From... the future. But wait! Here's the good part:"

And you proceed to show them cool stuff they have never seen before. Sadly, you are hampered by the lack of internet, lack of copy-paste, and don't want to look silly pulling folded pieces of paper out of your pocket. Remember, you represent... the future... so this had better be good. You decide on infinite growth patterns that you know by heart and can draw easily.

Easy to remember is not the same as small patterns, though there is some intersection. Start with the 5x5 infinite growth pattern (known result). That's small and not hard to memorize.

`x = 5, y = 5, rule = B3/S23`

3obo$o$3b2o$b2obo$obobo!

At this orientation, it looks to me like a minimalist landscape with a mountain at the bottom and something in the sky, perhaps the sun in the upper right. That sideways L could be clouds (YMMV). Pretty easy to remember one way or another, but a little hard to explain.

Most people have more experience memorizing symbols, so what if we try to keep a symbolic representation as small as possible. The smallest patterns don't have the smallest RLE necessarily. I can't guarantee this is minimal, but here is an infinite growth pattern with an 11-character RLE string that I found by enumeration. 11-characters is enough to encode very long lines, but this is a compromise in terms of encoding length and what you can enter.

`x = 22, y = 2, rule = B3/S23`

bo$8o3b11o!

I do not know if anyone else has done a search for short RLE. This is "new to me" as of this morning.

Still, the string "bo$8o3b11o!" is not very intuitive. Enter 7-segment display integers, encoded as 5x3 bitmaps. Dean Hickerson explored these some years back and found that 154299 was an infinite growth pattern in this simple "font" (and turns out to be pretty easy to enter by hand, but be sure to remember the lowest segment is lit on those 9s).

`x = 21, y = 5, rule = B3/S23`

ob3obobob3ob3ob3o$obo3bobo3bobobobobo$ob3ob3ob3ob3ob3o$o3bo3bobo5bo3bo

$ob3o3bob3ob3ob3o!

There is a smaller number, 140732, that works and somehow eluded DRH.

`x = 21, y = 5, rule = B3/S23`

obobob3ob3ob3ob3o$obobobobo3bo3bo3bo$ob3obobo3bob3ob3o$o3bobobo3bo3bob

o$o3bob3o3bob3ob3o!

I believe it was first mentioned on this blog.

But what about other things you can display with 7-segments? You can do hexadecimal, for one thing, if you don't mind mixing lowercase b and d with A, C, E, F. There were some old calculators that did this.

You can go down to 5 digits this way, and here are the examples of infinite growth I found. I did not find any with 4 digits, unfortunately:

20Ab1

`x = 19, y = 5, rule = B3/S23`

3ob3ob3obo5bo$2bobobobobobo5bo$3obobob3ob3o3bo$o3bobobobobobo3bo$3ob3o

bobob3o3bo!

99bC8

`x = 19, y = 5, rule = B3/S23`

3ob3obo3b3ob3o$obobobobo3bo3bobo$3ob3ob3obo3b3o$2bo3bobobobo3bobo$3ob

3ob3ob3ob3o!

b0bCd

`x = 19, y = 5, rule = B3/S23`

o3b3obo3b3o3bo$o3bobobo3bo5bo$3obobob3obo3b3o$obobobobobobo3bobo$3ob3o

b3ob3ob3o!

F7663

`x = 19, y = 5, rule = B3/S23`

3ob3ob3ob3ob3o$o5bobo3bo5bo$3o3bob3ob3ob3o$o5bobobobobo3bo$o5bob3ob3ob

3o!

My favorite is b0bCd. It's easy to remember and write. And it has a name: Bob.

How much further can we reduce the number of display digits? Here is a pattern that works with 3 7-segment display cells:

`x = 11, y = 5, rule = B3/S23`

4bobob3o$4bobo3bo$3ob3ob3o$2bo5bo$3ob3obo!

The only recognizable character is the rightmost, which can generously be called a question mark. So this one is small, but not really easy to memorize as a string.

Finally, here are some that encode an extended character set. These have all been used before on 7 segment displays. My favorite is probably _39-. That is easy to remember. AoCu is sort of cool, but would be much better if Ao was a chemical element (which it is not... Darn!).

5?28

`x = 15, y = 5, rule = B3/S23`

3ob3ob3ob3o$o5bo3bobobo$3ob3ob3ob3o$2bobo3bo3bobo$3obo3b3ob3o!

96u4

`x = 15, y = 5, rule = B3/S23`

3ob3o5bobo$obobo7bobo$3ob3obobob3o$2bobobobobo3bo$3ob3ob3o3bo!

AoCu

`x = 15, y = 5, rule = B3/S23`

3o5b3o$obo5bo$3ob3obo3bobo$obobobobo3bobo$obob3ob3ob3o!

_39-

`x = 15, y = 5, rule = B3/S23`

4b3ob3o$6bobobo$4b3ob3ob3o$6bo3bo$3ob3ob3o!