1. Koch Curve The Swedish mathematician Helge von Koch proposed the Koch curve in his 1904 paper “On a continuous curve without tangents, constructible from elementary geometry.” It is described as follows: Specify the length of a line segment \(l\) (this can be thought of as iteration 0) Divide this

1. Fractal Theory 1.1 The Definition of a Fractal A fractal usually refers to a geometric shape that can be divided into several parts, each of which is approximately a reduced-scale copy of the whole — that is, it has the property of self-similarity. 1.2 The History of Fractal Research In the 17th century, Leibniz already pondered the problem of self-similarity.