convolution (f * g)(t) = ∫f(τ)g(t-τ)dτ

How do different shapes combine to create new patterns?

Imagine you're mixing paints. You start with a small amount of blue and gradually add white paint. The resulting shade changes as you mix.

Convolution is like mixing paints. It combines two functions (like colors) to create a new function (a new shade). The formula f * g)(t) = ∫f(τ)g(t-τ)dτ shows how much of each function is combined at each point.

Example

If f(t) represents the amount of blue paint and g(t) represents the amount of white paint, the convolution f * g)(t) gives the total amount of paint mixed at time t.

Remember this

Convolution helps us understand how combining different functions (like mixing paints) results in a new function (a new shade).

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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