Fractal fans may well be fans of the droste effect. An image that has the Droste effect, depicts a smaller version of itself within its self. This smaller version then depicts an even smaller version of itself in the same place, and so on. Just like fractals. Therefore only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration exponentially reduces the picture’s size.
The effect is actually named after the image above. It appeared, with variations, on the tins and boxes of Droste cocoa powder. This was one of the main Dutch brands. It displays a nurse carrying a serving tray with a cup of hot chocolate and a box of the same brand. The brand’s effect, maintained for decades, became a household notion. Reportedly, poet and columnist Nico Scheepmaker introduced wider usage of the term in the late 1970s.
Here is an example of a Mandelbrot fractal that I have added the droste effect too.
and here it is after I animated it!