Abstract
Abstract We present two families of automatic sequences that define algebraic continued fractions in characteristic $2$. The period-doubling sequence belongs to the first family $\mathcal {P}$, and its sum modulo $2$, the Thue–Morse sequence, belongs to the second family $\mathcal {G}$. The family $\mathcal {G}$ contains all the iterated sums of sequences from the $\mathcal {P}$ and more.
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