  In this paper, we study 2d Floquet conformal field theory, where the external
periodic driving is described by iterated logistic or tent maps. These maps are
known to be typical examples of dynamical systems exhibiting the order-chaos
transition, and we show that, as a result of such driving, the entanglement
entropy scaling develops fractal features when the corresponding dynamical
system approaches the chaotic regime. For the driving set by the logistic map,
fractal contribution to the scaling dominates, making entanglement entropy
highly oscillating function of the subsystem size.
