I would like to show a mathematical way of evaluating the problem represented below:

The above image is formed due to the interference of incident and reflected light when a light source is kept at an angle with a curved surface , in this case is a cup.

I would care to explain how it does happen:

The diagram above is showing the reflection of a ray of light on a concave mirror ,and by geometry we can say that
arc(AO)=arc(OA’)This means that the reflected ray will cover twice the distance from where it bounces , i.e. ,the ray incident at point A reaches A’ and this covers distance of 2OA.

Fig-a

As if fig-a ,we draw a circle and lebel it with a lot of numbers.

Fig-b

In fig-b, we joined the number with the other number that comes when it is multiplied by 2 and if the product is greater than the largest number specified then we take the remainder with respect to the largest number specified . For example
2*2=4
15*2=30, 30>20,
and remainder in 30/20 is 10 .

Fig-c

In fig-c , when we increase the largest number specified we get this beautiful pattern.