# # 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).

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.