I mean universe - which stands continuously open to our gaze, but which cannot be understood unless one first learns to understand the language in which it is written. If you examine closely, the main branches growing out of a tree trunk, you will see that each looks like a smaller tree in itself, and so on as you look at smaller and smaller branches.
Clouds also express the self-similarity attribute.
In mathematics, however, a chaotic system is one whose behavior is unpredictable. A meteorologist named Edward Lorenz helped to pioneer the study of Chaos Theory when he discovered a disturbing fact. No matter how much information he gathered, his weather predications would quickly fail because there was no way he could use all of the variables of the weather. This is because the system will behave drastically differently with only slightly varying starting conditions. If air pressure, temperatures, and wind strength of Pittsburgh, PA, are only slightly affected, then tomorrow's weather could not be the same as today's weather.