Your Infinite Japanese Name

I saw on Facebook this code for converting your name into Japanese :

So, for example, Mike becomes Rin-Ki-Me-Ku.

Of course, there’s no reason to stop there. If my name is now RinKiMeKu, I can translate my name into Japanese again. Rin becomes ShiKiTo, Ki becomes MeKi, Me becomes RinKu and Ku becomes MeDo. So,

• My name is Mike.
• Therefore, my name is RinKiMeKu
• Therefore, my name is ShiKiToMeKiRinKuMeDo.

And, why stop there?

• Therefore, my name is AriRiKiMeKiChiMoRinKuMeKiShiKiToMeDoRinKuTeMo
• Therefore, my name is KaShiKiShiKiMeKiRinKuMeKiMiRiKiRinMoShiKiToMeDoRinKuMeKiAriR…
• Therefore, my name is MeKaAriRiKiMeKiAriRiKiMeKiRinKuMeKiShiKiToMeDoRinKuMeKiRinKi…

After that, my name starts to get quite long. If I kept up this trick, though, I’d start to see a pattern. The pattern would be more obvious if my name started with Z, say Zac or Zoe.

• First, my name would be Zac.
• Then, my name would be ZiKaMi.
• Then, my name would be ZiKiMeKaRinKi.
• Then, my name would be ZiKiMeKiRinKuMeKaShiKiToMeKi.
• Then, my name would be ZiKiMeKiRinKuMeKiShiKiToMeDoRinKuMeKaAriRiKiMeKiChiMoRinKuMe…
• Then, my name would be ZiKiMeKiRinKuMeKiShiKiToMeDoRinKuMeKiAriRiKiMeKiChiMoRinKuTe…
• Then, my name would be ZiKiMeKiRinKuMeKiShiKiToMeDoRinKuMeKiAriRiKiMeKiChiMoRinKuTe…
• Then, my name would be ZiKiMeKiRinKuMeKiShiKiToMeDoRinKuMeKiAriRiKiMeKiChiMoRinKuTe…

Now, the last few names are not the same. Each one is about 2-3 times longer than the one before. But the first 60 letters are the same. And once the first 60 letters stay the same, they always sty the same.

You can do this trick with other codes, say Morse Code. Let’s start with the famous message SOS, coded …—…

Then, you could code each dot as the word “dot” or “-..—-“, and each dash as the word “dash”, or “-…-…….”, getting longer and longer streams of dashes and dots, all but the first few starting -…-……. -..—- -..—- -..—- -…-……. -..—- (etc)

Taken to infinity, we get a well-defined pattern of dots and dashes that never repeats. It’s not random, it’s not regular. It has just the right mixture of chaos and order to be interesting.

Once you get the idea of this, you can do this trick with any way of coding a bunch of symbols into a bunch of similar symbols. See, for example, the infinite music I made from Twinkle Twinkle Little Star.