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.

翻译：在星际通信的语境下，我们事先无法预知给定信号的接收者是否为植物、昆虫，甚至地球科学家未知的生命形式。无论情况如何，消息的时间尺度可能过快或过慢，导致这些生物可能永远无法解码。因此，设计一种与时间尺度无关的消息编码方法具有重要意义。分形消息因其结构自相似性（有时还具备尺度不变性）而能实现这一目标。从空间嵌入的逻辑出发，本文构建了一种无时间尺度的消息传输框架。当考虑与时间无关的消息传输框架时，理想的方式是将消息编码为可在多个时空尺度上解码的形式。为此，本文提出的核心思路是：将二进制消息编码为沿无穷多个（呈幂律分布的）频率和振幅传播的波，传输该消息，再完成解码与复现。具体实现中，采用已知分形——魏尔斯特拉斯函数的各分量作为消息载体，通过对每个分量的振幅进行调制以嵌入二进制数据流，从而实现与时间无关的消息传递方案。