  In many communication contexts, the capabilities of the involved actors
cannot be known beforehand, whether it is a cell, a plant, an insect, or even a
life form unknown to Earth. Regardless of the recipient, the message space and
time scale could be too fast, too slow, too large, or too small and may never
be decoded. Therefore, it pays to devise a way to encode messages agnostic of
space and time scales. We propose the use of fractal functions as
self-executable infinite-frequency carriers for sending messages, given their
properties of structural self-similarity and scale invariance. We call it
`fractal messaging'. Starting from a spatial embedding, we introduce a
framework for a space-time scale-free messaging approach to this challenge.
When considering a space and time-agnostic framework for message transmission,
it would be interesting to encode a message such that it could be decoded at
several spatio-temporal scales. Hence, the core idea of the framework proposed
herein is to encode a binary message as waves along infinitely many frequencies
(in power-like distributions) and amplitudes, transmit such a message, and then
decode and reproduce it. To do so, the components of the Weierstrass function,
a known fractal, are used as carriers of the message. Each component will have
its amplitude modulated to embed the binary stream, allowing for a
space-time-agnostic approach to messaging.
