Enzymind Labs

Background and term links. These are mostly Wikipedia entries. Mathworld is also an excellent source of information for many of the topics:

Pinwheel tiling

Quaquaversal tiling

Substitution tilings

Analytic number theory

Circle Maps

Euler-Massheroni constant

"The two constants are also related by the pair of series (see Sondow 2005 #2)

where N₁(n) and N₀(n) are the number of 1's and 0's, respectively, in the base 2 expansion of n."

This is interesting because the Thue-Morse sequence can be found by modular arithmetic on the base 2 expansion of n (sum of the first n digits). From Thue-Morse:

"To compute the nth element t_n, write the number n in binary. If the number of ones in this binary expansion is odd then t_n = 1, if even then t_n = 0. For this reason John H. Conway et al. call numbers n satisfying t_n = 1 odious numbers and numbers for which t_n = 0 evil numbers."

Is there a closed form functional relationship between the Prouhet-Thue-Morse constant and the Euler-Massheroni constant?

Euler's theorem

Fibonacci number

Ford circles

Generalised Morse sequence

Limit set

Logistic map

L-System

Minkowski question mark function

Modular arithmetic

Modular groups

Modular group (dyadic monoid)

Multiplicative group of integers modulo n

Periodic point

Procedural generation

Procedural texture

Prouhet-Thue-Morse sequence

Quasicrystals

Renormalization group

Shapiro polynomials

String rewriting system