A general conceptual understanding of moving average
That system you're referring to is a first-order recursive filter

$$y[n]=\alpha x[n]+(1-\alpha)y[n-1],\qquad 0&lt;\alpha&lt;1\tag{1}$$

where $n$ is the (integer) time index, $y[n]$ is the output, and $x[n]$ is the input. You chose $\alpha=\frac12$.

That filter is also called exponentially weighted moving average. It has theoretically infinite memory and weighs the past input values with exponentially decreasing weights.