Scale invariance

Several decades ago, physicists and mathematicians started to study problems that had typically belonged to other fields. There are some geometric structures that frequently appear in those fields like biology or economy. We are talking about fractals. Let’s try to understand what properties are related to those figures and how we can recognize them. 

What are the similarities between the images below? 

In the first picture, we can see a nurse carrying a Droste cocoa package where the same picture recursively appears. The same happens in the second picture. In fact, this strategy has been extensively used with a commercial purpose. Nowadays, we call this the “Droste effect” after the Dutch brand of cocoa that first came up with it.

Nevertheless, this effect has also been used by artists like painters or … singers! In The visage of War, painted in 1940, Salvador Dalí makes use of self-similarity in order to express the suffering of the Spanish population during the Civil War. The infinite iteration of horrified faces reflects the large number of crimes that were committed during the conflict.

If you are a 60’s music fan you will be able to recognize the other picture. Actually, it is the cover artwork from the fourth Pink Floyd’s album “Ummagumma” released on 7 November 1969. It shows a Droste effect featuring the group, with a picture hanging on the wall showing the same scene, except that the band members have switched positions.