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## Infinite growth 7-segment integers (variable width)

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Infinite growth 7-segment integers (variable width)

dvgrn pointed out that my 7-segment display characters were using fixed width, causing 1 to be spaced farther from other digits than needed. That was intentional, since it's how old 7-segment displays really work, but I adapted the code to get integers with compressed spacing and ran them for infinite growth up to a million. At least two of these are known. 154299 due to Dean Hickerson, and 140732 (infinitegrowth wordpress blog, author unknown). 832021 and its mirror image 835051 both produce infinite gliders.

140732
`x = 21, y = 5, rule = B3/S23obobob3ob3ob3ob3o\$obobobobo3bo3bo3bo\$ob3obobo3bob3ob3o\$o3bobobo3bo3bobo\$o3bob3o3bob3ob3o!`

154299
`x = 21, y = 5, rule = B3/S23ob3obobob3ob3ob3o\$obo3bobo3bobobobobo\$ob3ob3ob3ob3ob3o\$o3bo3bobo5bo3bo\$ob3o3bob3ob3ob3o!`

367021
`x = 21, y = 5, rule = B3/S233ob3ob3ob3ob3obo\$2bobo5bobobo3bobo\$3ob3o3bobobob3obo\$2bobobo3bobobobo3bo\$3ob3o3bob3ob3obo!`

601986
`x = 21, y = 5, rule = B3/S233ob3obob3ob3ob3o\$o3bobobobobobobobo\$3obobobob3ob3ob3o\$obobobobo3bobobobobo\$3ob3obob3ob3ob3o!`

832021
`x = 21, y = 5, rule = B3/S233ob3ob3ob3ob3obo\$obo3bo3bobobo3bobo\$3ob3ob3obobob3obo\$obo3bobo3bobobo3bo\$3ob3ob3ob3ob3obo!`

835051
`x = 21, y = 5, rule = B3/S233ob3ob3ob3ob3obo\$obo3bobo3bobobo3bo\$3ob3ob3obobob3obo\$obo3bo3bobobo3bobo\$3ob3ob3ob3ob3obo!`

979374
`x = 23, y = 5, rule = B3/S233ob3ob3ob3ob3obobo\$obo3bobobo3bo3bobobo\$3o3bob3ob3o3bob3o\$2bo3bo3bo3bo3bo3bo\$3o3bob3ob3o3bo3bo!`

986109
`x = 21, y = 5, rule = B3/S233ob3ob3obob3ob3o\$obobobobo3bobobobobo\$3ob3ob3obobobob3o\$2bobobobobobobobo3bo\$3ob3ob3obob3ob3o!`

I also tried padding with leading zeros and that does not produce additional infinite growth patterns.
pcallahan

Posts: 298
Joined: April 26th, 2013, 1:04 pm

### Re: Infinite growth 7-segment integers (variable width)

I was also curious about infinite growth in the decimal expansion of π, which I know is useless and arbitrary (and too early even for π-day this year but I can't wait).

64715509 is 8 digits starting at position 4386 in the decimal expansion of π. You can verify here.
`x = 29, y = 5, rule = B3/S233obobob3obob3ob3ob3ob3o\$o3bobo3bobobo3bo3bobobobo\$3ob3o3bobob3ob3obobob3o\$obo3bo3bobo3bo3bobobo3bo\$3o3bo3bobob3ob3ob3ob3o!`

The six-digit infinite growth numbers show up in the first half million or so digits, but that is unsurprising. I increased the window to find something earlier. After 8 digits, going up to 50, nothing else shows up at 4386 or earlier except extensions of the 8 digits. At this point, they become hard to draw manually, so I think 64715509 is a good place to stop. I may keep looking for a longer one though.
pcallahan

Posts: 298
Joined: April 26th, 2013, 1:04 pm

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