# Tuning

Given a periodic external angle pair $(.\overline{a}, .\overline{b})$ , tuning of an external angle $.c$ proceeds by replacing every $0$ in $c$ by $a$ and every $1$ by $b$ . Here $a$ , $b$ , $c$ are blocks of binary digits (with $c$ possibly aperiodic and infinite in extent).

# 1 Haskell Code

type ExternalAngle = ([Bool], [Bool])

tuning
  :: (ExternalAngle, ExternalAngle)
  -> ExternalAngle
  -> ExternalAngle
tuning (([], per0), ([], per1)) (pre, per)
  = (concatMap t pre, concatMap t per)
  where
    t False = per0
    t True  = per1

# 2 Examples

The external angle pair of the period $3$ island is: $\left(.\overline{011}, .\overline{100}\right)$

The lower angle of the period $2$ bulb is $.\overline{01}$ , tuned by the period $3$ island becomes $.\overline{011100}$ which is the lower angle of the period $6$ bulb attached to the period $3$ cardioid at internal angle $\frac{1}{2}$ .

The external angle of the tip of the antenna is $.1 = .0\overline{1} = .1\overline{0}$ , tuned by the period $3$ island becomes respectively $.011\overline{100}$ and $.100\overline{011}$ , which are the external angles of the tip of the antenna of the period $3$ island.