If you see it and manipulate it then you really understand it

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Visual thinking has been around since the Greeks' passion for eidos (idea). But of course computers have transformed it into an art, whose dynamic simulations and graphic representations of concepts and abstract entities is orders of magnitude more effective and impressive than anything done in the past. This website, for example, offers some remarkable pictures that visualise prime numbers and their beautiful patterns.

If you find the topic interesting, then I may recommend Modelling Reality - How Computers Mirror Life. It is a very well-written, interesting and accessible text on how computers have transformed our way of dealing with the world of information, including cellular automata, Shannon's measure of information, deterministic chaos, fractals, game theory, neural networks, genetic algorithms, and of course Turing machines. It comes with a CD full of applications that actually allow you to experiment and see the processes and theories discussed.

And if you share my fascination with computational modelling, then you cannot miss The Philosophical Computer. The book presents a series of exploratory essays on how computational modelling can help to tackle a variety of issues in philosophy and in philosophical logic, including self-reference, fuzzy logic, epistemic chaos, and cellular automata in game theory, dealing with generosity, possible causes and cures for discrimination, and the formal undecidability of patterns of social and biological interaction. The book comes with a CD containing and the source code of all major programs to facilitate further research.

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