Emergence
Emergence occurs when properties or behaviors arise, through a specific configuration or interaction, from something that doesn't have those properties or behaviors. For example, possessing only a ganglia of nerves, an individual bee doesn't have the necessary intelligence to create a complex hexagonal lattice structure known as a hive, but, if thousands of bees work together, a hive will emerge from their efforts.
Emergence arises in pretty much all interactions be they living or non-living, conscious or unconscious. Wind, water, and sand will often create highly intricate repeating patterns, flocking animals will behave like larger structures, simple mathematical formulas when graphed will reveal an unpredicted framework, etc.
Emergence helps us to make sense of the world. When we understand that complex systems are governed by comparatively simple rules, it becomes much easier to model those systems and study the emergent properties that arise at the larger scale. When we're able to do this, we can make drastically better predictions about complex systems like weather, fluid motion, the structure of galaxies, animal behavior, and even the formation of life and consciousness.
Contents
Personal
I was fascinated with emergence long before I knew there was a name for it. I remember seeing casts of ant nests and videos of flocking birds and being amazed how, even though the animals themselves don't know how to create such intricate patterns, the patterns still arise. I was especially interested in fractals and wanted to know how they worked, and was again surprised to learn how simple they are. As I slowly became less religious, and found religious apologetics unsatisfactory, I sought secular answers to the more complex questions like "how did we get here?" which eventually led me to discovering the name for complexity arising from simplicity. The more I learn about emergence, the more I'm utterly blown away by it.
Examples
Emergence occurs in pretty much every system including language, city planning, animal migration and flocking, mathematics, weather, embryonic development, etc. I find all of these fascinating, but the areas of emergence that relate to fractals and cellular automation are the ones I find especially interesting.
Media
In the Mandelbrot set, a simple mathematical algorithm, when plotted, exhibits vast repetitive complexity.