Fractal time scale-free agnostic messaging: amplitude modulation of carriers given by the Weierstrass function's components

In the context of interstellar communication, it is not known beforehand if the receiver of a given signal would be a plant, an insect, or even life forms unknown to terrestrial scientists. Regardless of the situation, the message time scale could be too fast or too slow and those beings would probably never decode it. Therefore, it is of interest to devise a way to encode messages agnostic of time scale. Fractal messaging would allow one to do this due to their structural self-similarity and, sometimes, scale invariance. By starting from a spatial embedding rationale, a framework is developed for a time scale-free messaging alternative. When one considers a time-agnostic framework for message transmission, it would be interesting to encode a message such that it could be decoded along several spatio-temporal scales. This way, the core idea of the framework hereby proposed is to encode a binary message as waves along infinitely many (power-like distributed) frequencies and amplitudes, transmit such message, and then decode and reproduce it. To do so, the components of the Weierstrass function, a known fractal, are used as the carriers of the message. Each component will have its amplitude modulated to embed the binary stream, allowing for a time-agnostic approach to messaging.