Does every group have a leader? Does every pattern have a central cause? Most people tend to think so. Increasingly, decentralized models are being chosen for the organizations and technologies they construct in the world, and for the theories they construct about the world. But even as ideas about decentralization spread throughout the culture, there is a deep-seated resistance to them. This text examines how and why this is so and describes innovative computational tools and activities that can help people (even young children) develop new ways of thinking about decentralization, with examples in many different domains. This wide-ranging exploration into the non-intuitive world of decentralized systems and self-organizing phenomena brings together ideas from computer science, education, systems theory, and artificial life, with the aim of making the notion of self-organization more accessible. Using a new massively parallel programming language called StarLogo, Mitchel Resnick shows how the actions and interactions of thousands of artificial "creatures" can be controlled on the computer screen. For example, a user might write simple programs to describe the actions of thousands of artificial ants, then observe the complex patterns in the ant colony that arise from all of the interactions. Resnick describes how high school students have used StarLogo to create new types of computer simulations, examines how their thinking changed in the process, and concludes by proposing heuristics for thinking about decentralized systems.