Final answer:
Waves sort themselves out from 'chaos' to 'order' through dispersion, where different wavelengths travel at different speeds and separate. Examples include rainbows and sound through a tube. Chaos can also show self-organization, creating order within complex systems like planetary orbits and Jupiter's Great Red Spot.
Step-by-step explanation:
Dispersing waves sort themselves out from 'chaos' to 'order' through a process known as dispersion. This occurs when waves spread out due to their speed of propagation depending on their wavelength. When different wavelengths of a wave travel at different speeds, they separate from one another, creating a display of 'ordered' wave patterns from what initially seems chaotic. An example of dispersion is the production of a rainbow, where sunlight is dispersed into its constituent colors or wavelengths. Another example is when sound waves are dispersed by travelling through a long tube, like a vacuum cleaner hose, changing the way the sound is heard based on how different frequencies are spread out.
Moreover, the concept of chaos in relation to complexity explains that while systems may appear chaotic, they can exhibit self-organization and form patterns that seem organized and orderly. For example, planetary orbits show systematic behavior despite underlying chaotic properties. This type of stable chaos is also found in phenomena like the Great Red Spot on Jupiter, a long-lasting vortex exhibiting organized behavior despite the complex and chaotic atmospheric conditions.