Curves - Monster

The concept of Monster Curves dates back to the early 20th century, when mathematicians like Wacław Sierpiński and Helge von Koch began exploring the properties of fractals. However, it wasn't until the 1970s that the term "Monster Curve" was coined by mathematician and science writer, Martin Gardner. Gardner used this term to describe a specific type of fractal curve, known as the "Menger sponge," which was constructed by Austrian mathematician Walter Menger in the 1920s.

Monster Curves have several interesting properties, including: monster curves

The true depth of Monster Curves is revealed through Benoit Mandelbrot’s fractal geometry, which provided the language to tame these beasts. The concept of Monster Curves dates back to

A "Monster Curve" is formally defined as a continuous curve that exhibits properties previously thought to be contradictory or impossible. These include curves that are everywhere continuous but nowhere differentiable, curves of infinite length enclosing finite area, and curves that possess a non-integer topological dimension. $$ N \propto \frac{1}{s^{D_H}} $$

$$ N \propto \frac{1}{s^{D_H}} $$