Indu Satija celebrates the 50th anniversary of the publication of Douglas Hofstadter’s eponymous, iconic butterfly and explains its enduring, magnetic appeal

Animal magic An early version of the butterfly diagram, created by Douglas Hofstadter in 1975, showing the energy ( x -axis) of electrons moving in a 2D lattice under an applied magnetic field ( y -axis). (CC BY SA 3.0 Douglas Hofstadter)"> Animal magic An early version of the butterfly diagram, created by Douglas Hofstadter in 1975, showing the energy ( x -axis) of electrons moving in a 2D lattice under an applied magnetic field ( y -axis). (CC BY SA 3.0 Douglas Hofstadter)

In the mid-1970s a graduate student wrestling with a deceptively simple quantum problem uncovered one of the most haunting images in modern physics. The pattern seemed almost impossibly intricate: delicate wings assembled from infinitely nested bands and gaps, a self-similar pattern born from the motion of electrons in a crystal under a magnetic field.…