What's up with the "2-bit ruler"?

[Saka]

What's up with the "2-bit ruler" I've seen in some people's signatures? Although I am considered a geek, what is a 2 bit ruler???

[blah]

You mean a base 2 ruler?

Code: Select all

x = 32, y = 5, rule = B3/S23
bobobobobobobobobobobobobobobobo$2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$4b4o4b4o4b4o4b4o$8b8o8b8o$16b16o!

It's just the binary numberline, if that's what you mean.

[Saka]

You mean a base 2 ruler?

Code: Select all

x = 32, y = 5, rule = B3/S23
bobobobobobobobobobobobobobobobo$2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$4b4o4b4o4b4o4b4o$8b8o8b8o$16b16o!

It's just the binary numberline, if that's what you mean.

Ah yes base 2 not 2 bit. My mistake

[gameoflifeboy]

I saw that and I realized that since binary counting is just expressing each number as a sum of powers of two, one could express each number as a sum of different numbers and get a different pattern. So I made one where each number was expressed as the sum of central polygonal numbers (which are one more than the triangular numbers) and put as much of it as I could in my signature.

Since there are many ways to give each number as a sum of central polygonal numbers, I created my sums by taking the largest central polygonal number t1 less than a number n, adding the largest central polygonal number t2 less than n - t1, adding the largest central polygonal number t3 less than n - t1 - t2, and so on. (I think this is called the greedy algorithm.)

Each column represented a natural number and each row represented a central polygonal number. Here is a longer ruler:

Code: Select all

x = 1081, y = 46, rule = B3/S23
obobo2bobobobo2bobobobobobo2bobobo3bobobo2bobobobo2bo2bobobo2bobobobob
o2bobo2bobobo2bobobobobobo2bobobo2bobobo2bobobobobobobo2bobobobo2bobob
o2bobobobo3bobobo2bobobobo2bobobobo2bobobobo2bo2bobobo2bobobobo2bobobo
bobo2bobobobo2bobo2bobobo2bobobobo2bobobobobobo2bobobobo2bobobo2bobobo
2bobobobo2bobobobobobobo2bobobobo2bobobobo2bobobo2bobobobo2bobobobobob
obobo2bobobobo2bobobobobo2bobobo2bobobobo2bobobobobobobobobo2bobobobo
2bobobobobobo2bobobo2bobobobo2bobobobobobo3bobobo2bobobobo2bobobobobob
o2bobobobo2bobobobo2bobobobobobo2bo2bobobo2bobobobo2bobobobobobo2bobob
obobo2bobobobo2bobobobobobo2bobo2bobobo2bobobobo2bobobobobobo2bobobobo
bobo2bobobobo2bobobobobobo2bobobo2bobobo2bobobobo2bobobobobobo2bobobo
3bobobo2bobobobo2bobobobobobo2bobobo4bobobo2bobobobo2bobobobobobo2bobo
bo3bobobobo2bobobobo2bobobobobobo2bobobo3bo2bobobo2bobobobo2bobobobobo
bo2bobobo3bobobobobo2bobobobo2bobobobobobo2bobobo3bobo2bobobo2bobobobo
2bobobobobobo2bobobo3bobobobobobo2bobobobo2bobobobobobo2bobobo3bobobo
2bobobo2bobobobo2bobobobobobo2bobobo3bobobo3bobobo2bobobobo2bobobobobo
bo2bobobo3bobobo2bo$b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo3b2o2bo4b2o2bo2bo
2b2o2bo2b2o2b2o2bo2b2o3b2o2bo2b2o4b2o2bo2b2o2bo2b2o2bo2b2o2b2o2b2o2bo
2b2o2b2o3b2o2bo2b2o2b2o4b2o2bo2b2o2b2o5b2o2bo2b2o2b2o3bo2b2o2bo2b2o2b
2o3b2o2b2o2bo2b2o2b2o3b2o3b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2b2o3b2o5b2o2bo
2b2o2b2o3b2o6b2o2bo2b2o2b2o3b2o4bo2b2o2bo2b2o2b2o3b2o4b2o2b2o2bo2b2o2b
2o3b2o4b2o3b2o2bo2b2o2b2o3b2o4b2o4b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo2b2o
2b2o3b2o4b2o2bo3b2o2bo2b2o2b2o3b2o4b2o2bo4b2o2bo2b2o2b2o3b2o4b2o2bo2bo
2b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2b2o2bo2b2o2b2o3b2o4b2o2bo2b2o3b2o2bo2b
2o2b2o3b2o4b2o2bo2b2o4b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo2b2o2bo2b2o2b2o
3b2o4b2o2bo2b2o2bo3b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo4b2o2bo2b2o2b2o3b2o
4b2o2bo2b2o2bo5b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo3bo2b2o2bo2b2o2b2o3b2o
4b2o2bo2b2o2bo3b2o2b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo3b2o3b2o2bo2b2o2b2o
3b2o4b2o2bo2b2o2bo3b2o4b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo3b2o2bo2b2o2bo
2b2o2b2o3b2o4b2o2bo2b2o2bo3b2o2bo3b2o2bo2b2o2b2o3b2o4b2o2bo2b2o2bo3b2o
2bo$3b3o8bo4b2o4b3o4b3o5b3o6b3o7b3o8b3o9b3o10b3o11b3o12b3o8bo4b3o8bo5b
3o8bo6b3o8bo7b3o8bo8b3o8bo4bo4b3o8bo4b2o4b3o8bo4b2o5b3o8bo4b2o6b3o8bo
4b2o7b3o8bo4b2o8b3o8bo4b2o4bo4b3o8bo4b2o4b2o4b3o8bo4b2o4b3o4b3o8bo4b2o
4b3o5b3o8bo4b2o4b3o6b3o8bo4b2o4b3o7b3o8bo4b2o4b3o8b3o8bo4b2o4b3o4bo4b
3o8bo4b2o4b3o4b2o4b3o8bo4b2o4b3o4b3o4b3o8bo4b2o4b3o4b3o5b3o8bo4b2o4b3o
4b3o6b3o8bo4b2o4b3o4b3o7b3o8bo4b2o4b3o4b3o8b3o8bo4b2o4b3o4b3o9b3o8bo4b
2o4b3o4b3o5bo4b3o8bo4b2o4b3o4b3o5b2o4b3o8bo4b2o4b3o4b3o5b3o4b3o8bo4b2o
4b3o4b3o5b3o5b3o8bo4b2o4b3o4b3o5b3o$6b4o25bo7b2o7b3o7b4o7b4o8b4o9b4o
10b4o11b4o12b4o13b4o14b4o15b4o16b4o17b4o18b4o19b4o20b4o21b4o22b4o23b4o
24b4o25b4o26b4o27b4o28b4o29b4o30b4o31b4o32b4o25bo7b4o25bo8b4o25bo9b4o
25bo10b4o25bo11b4o25bo12b4o25bo13b4o25bo14b4o25bo7bo7b4o25bo7b2o$10b5o
62bo11b2o11b3o11b4o11b5o11b5o12b5o13b5o14b5o15b5o16b5o17b5o18b5o19b5o
20b5o21b5o22b5o23b5o24b5o25b5o26b5o27b5o28b5o29b5o30b5o31b5o32b5o33b5o
34b5o35b5o36b5o37b5o38b5o39b5o40b5o$15b6o131bo16b2o16b3o16b4o16b5o16b
6o16b6o17b6o18b6o19b6o20b6o21b6o22b6o23b6o24b6o25b6o26b6o27b6o28b6o29b
6o30b6o31b6o32b6o33b6o34b6o35b6o36b6o37b6o38b6o39b6o$21b7o247bo22b2o
22b3o22b4o22b5o22b6o22b7o22b7o23b7o24b7o25b7o26b7o27b7o28b7o29b7o30b7o
31b7o32b7o33b7o34b7o35b7o36b7o37b7o38b7o$28b8o428bo29b2o29b3o29b4o29b
5o29b6o29b7o29b8o29b8o30b8o31b8o32b8o33b8o34b8o35b8o36b8o37b8o$36b9o
695bo37b2o37b3o37b4o37b5o37b6o37b7o37b8o37b9o$45b10o$55b11o$66b12o$78b
13o$91b14o$105b15o$120b16o$136b17o$153b18o$171b19o$190b20o$210b21o$
231b22o$253b23o$276b24o$300b25o$325b26o$351b27o$378b28o$406b29o$435b
30o$465b31o$496b32o$528b33o$561b34o$595b35o$630b36o$666b37o$703b38o$
741b39o$780b40o$820b41o$861b42o$903b43o$946b44o$990b45o$1035b46o!