Never heard the name before, but as the Wikipedia page on the Droste effect explains, it’s a pretty familiar concept:
The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. 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 geometrically reduces the picture’s size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry.
The effect is named after the image on the tins and boxes of Droste cocoa powder, one of the main Dutch brands, which displayed a nurse carrying a serving tray with a cup of hot chocolate and a box with the same image. This image, introduced in 1904 and maintained for decades with slight variations, became a household notion. Reportedly, poet and columnist Nico Scheepmaker introduced wider usage of the term in the late 1970s.
The Droste effect was used by Giotto di Bondone in 1320, in his Stefaneschi Triptych. The polyptych altarpiece portrays in its center panel Cardinal Giacomo Gaetani Stefaneschi offering the triptych itself to St. Peter. There are also several examples from medieval times of books featuring images containing the book itself or window panels in churches depicting miniature copies of the window panel itself. See the collection of articles Medieval mise-en-abyme: the object depicted within itself for examples and opinions on how this effect was used symbolically.
I vaguely recall it first making an impression on me on the front of some 1970s Blue Peter annual I picked up at a jumble sale or boot fair…
From a quick google I see that the Blue Peter annual has been axed.
I knew it! Here’s the Blue Peter annual cover I was thinking of (image via Nigel’s WebSpace Galleries Of Annuals) – the tenth one, from 1973.