# # 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.