@k0sm0naut to A place for everything about math • 3 years agoThue-Morse Adjacent Fractal (made from turtle graphics on Mathematica)imgur.comexternal-linkmessage-square2arrow-up13arrow-down10
arrow-up13arrow-down1external-linkThue-Morse Adjacent Fractal (made from turtle graphics on Mathematica)imgur.com@k0sm0naut to A place for everything about math • 3 years agomessage-square2
minus-square@k0sm0nautOPlink2•3 years agoSo, usually the Thue-Morse sequence is created by the morphism 0 -> 01, 1 -> 10. This ends up creating the Koch snowflake using turtle graphics. But, I thought it might be interesting to change the morphism so the 0 alternates between 00 and 01 and 1 -> 10/11. Here are the first 100 terms: 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0
So, usually the Thue-Morse sequence is created by the morphism 0 -> 01, 1 -> 10. This ends up creating the Koch snowflake using turtle graphics.
But, I thought it might be interesting to change the morphism so the 0 alternates between 00 and 01 and 1 -> 10/11.
Here are the first 100 terms: 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0
Does anyone know how you would refer to such a morphism?