Newton FractalNewton’s root-finding method is the trick your calculator uses to solve equations: guess, follow the slope, repeat. Colour every starting guess by which solution it ends up at and the map of “who goes where” turns out to have an infinitely crinkled coastline.Newton and Raphson published the method around 1690 as pure arithmetic. In 1879 Arthur Cayley tried to work out its behaviour for every complex starting point; he cracked the quadratic, then wrote that the cubic “presents difficulty” — the difficulty being a fractal, a word that did not exist for another century.