You may remember doing quadratic equations at school - or some of you may be engineers or scientists and use quadratics regularly. The problem with them was always that a very large number cannot be solved - or they can be solved, but they give 'complex' answers.
Lorentz noticed that even though he was using fairly simple, well understood equations, the computer sometimes returned wildly fluctuating results which didn't seem to settle on a single value. He also noticed that if he changed the starting conditions very slightly, the results would be hugely different. Lorentz had discovered what later became known as Chaos theory - the branch of mathematics which is concerned with apparently simple and completely understood equations and models that, nevertheless, could turn into spiteful unpredictable monsters out of nowhere. They are NOT RANDOM - chaotic systems do not have random elements in them, they are completely deterministic.
You might think that there is surely some contradiction here. How can an equation, where we know all the terms exactly, produce results which we cannot predict?
The answer is that very tiny changed in the initial conditions are amplified to produce massive differences in the final output. This was labelled the 'butterfly effect' - the idea being that the flap of a butterfly wing could be sufficient to produce a hurricane in some other location, as the weather system amplified the tiny variation. The type of system where this happens is characterised by what an engineer would call a feedback mechanism and what a mathematician would call an iterative function. ie The output somehow influences the next input. Usually systems producing this type of thing are designed to converge on equilibrium (a single 'value' of output) and the output is fed-back into the system in a way which evens things out. If the output starts rising, the feedback mechanism should cause it to fall. If it starts to fall then the feedback should increase it.
If you want a simple image of this then consider a simple heating system with a boiler, some radiators and a thermostat. The thermostat is the feedback mechanism - it links the output of the system (heat) to the input of the system (the burning of fuel at the boiler). The simplest type of system is binary - the thermostat is designed to send a signal when the temperature reaches a set level. This signal stops the flow of fuel to the boiler and therefore stops the heating process. When the temperature drops below the set level then the thermostat stops sending the signal, the fuel resumes and the boiler goes back to producing heat. Such a system would, in fact, be horribly inefficient because the boiler would be coming on and off in short bursts as the temperature fluctuated around the trigger. This is a very inefficient way to run a boiler - a large amount of the heat produced is wasted to the environment, and not directed to the radiators. The system would, however, function to keep the temperature very close to the set value. This type of feedback is called negative feedback and will always tend to an equilibrium state.
The opposite - a positive feedback system - will tend to an exponentially rising output. Most people are familiar with a good example of this that often occurs when a microphone is too close to the speakers which are projecting the amplified sound. Some of the amplified signal enters the microphone, which then goes through the amplifiers and is boosted to produce more sound at the speaker. This in turn increases the sound output and more sound goes back into the microphone - the result is a runaway cascade which we call simply 'feedback'.
Most of the time audio feedback just produces a horrible squealing sound before it either blows something or the microphone is moved. It can be used, however, by musicians who know what they are doing to contribute to the piece. The first example that I know of (and this is generally agreed by sound engineers) is from the Beatles in 1964, at the start of the track I Feel Fine