Avoidability of Additive Cubes over Alphabets of Four Numbers

Extending Dekking's construction of an infinite binary word avoiding abelian $4$-powers

“…Over the alphabet {0, 1}, a word is an abelian k-power if and only if it is an additive k-power, but on larger alphabets these two notions are no longer equivalent. Three important papers on the avoidance of additive powers are: the paper of Cassaigne, Currie, Schaeffer, and Shallit [2], the paper of Rao and Rosenfeld [11], and the paper of Lietard and Rosenfeld [9].…”