I've recently been experimenting with Conway's Game of Life and am captivated by the concept of emergence that it operates on. It is the idea that predictable and relatively simple rules can lead to complex and often unpredictable outcomes. The properties exhibited by the emergent entity can't be found in the individual rules or components that make up and lead to the entity.
You can find emergence everywhere, from biological to computing systems. The simple mathematical neurons that form an entire artificial neural network trained to make predictions. Similarly*, electrochemical neurons, through their interactions, give rise to the sophisticated functions of the human brain. The tiny transistors in an integrated circuit that make simple logic gates and the functional blocks they make, like adders and decoders, when used in conjunction with one another. Emergence can also be seen in evolution, a fascinating example is the branching fractal structures of an early group of organisms called Rangeomorphs.
* Although the artificial neuron was inspired by its biological counterpart, with its beginnings in the 1940s through the ideas of Warren McCulloch, Walter Pitts, and Donald Hebb, and later implemented in hardware by Frank Rosenblatt as the single-layer perceptron in 1957, it remains completely distinct from its biological equivalent and is purely a mathematical construct.