The undisputed king of the flashing lights is the strobe light.
This page discusses theory of operation. For some commercial products, please see commercial flashers.
Consider these strips of metal that are the same length at 70 degrees.
When you raise the temperature, you find that both strips expand, but due to the different types of metal used, the red strip expands to a greater length.
At lower temperatures, the red strip also shrinks faster.
But if you fasten the strips together when the temperature is 70 degrees,
heating will make the red side of the strip want to expand to a greater length than the other.
As the two-metal strip gets hotter, the red side grows longer than the blue side, pushing the strip to the left.
As the two-metal strip gets cooler, the red side grows shorter than the blue side, pushing the strip to the right.
A bi-metallic strip that pushes to one side or the other in response to temperature is a classic way to make a thermostat. It is also the basis of the blinking Christmas tree lamp, and other flashers:
Here's a simple strobe, with the relaxation oscillator near the center, enclosed in a rectangle.
The relaxation oscillator consists of few components:
It looks like a LED, it lights up like a LED, it comes in assorted colors like a LED, it consumes low power like a LED - but it has a built-in timer chip that turns the LED on and off. The only drawback to the self-flashing LED is that you don't get any real control over the rate at which it flashes. It does what the guys at the factory like it to do.
Note that you can put an ordinary LED and a flasher in series, and then both will flash.
There is an excellent 555 timer tutorial at
http://www.uoguelph.ca/~antoon/gadgets/555/555.html
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