section_path: Role and characterizations in mathematics/In the Mandelbrot set
section_name: In the Mandelbrot set
paragraph_text: In the Mandelbrot set
  
  An occurrence of π in the fractal called the Mandelbrot set was discovered by David Boll in 1991. He examined the behaviour of the Mandelbrot set near the "neck" at (−0.75, 0). When the number of iterations until divergence for the point (−0.75, ε) is multiplied by ε, the result approaches π as ε approaches zero. The point (0.25 + ε, 0) at the cusp of the large "valley" on the right side of the Mandelbrot set behaves similarly: the number of iterations until divergence multiplied by the square root of ε tends to π.