k0sm0naut@lemmy.ml to A place for everything about math@lemmy.ml · 3 years agoThue-Morse Adjacent Fractal (made from turtle graphics on Mathematica)imgur.comexternal-linkmessage-square2fedilinkarrow-up13arrow-down10
arrow-up13arrow-down1external-linkThue-Morse Adjacent Fractal (made from turtle graphics on Mathematica)imgur.comk0sm0naut@lemmy.ml to A place for everything about math@lemmy.ml · 3 years agomessage-square2fedilink
minus-squarek0sm0naut@lemmy.mlOPlinkfedilinkarrow-up2·3 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
minus-squarek0sm0naut@lemmy.mlOPlinkfedilinkarrow-up1·3 years agoDoes anyone know how you would refer to such a morphism?
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?