The document discusses the Minkowski curve, a fractal curve first introduced by Hermann Minkowski. It has the property of self-similarity, where portions of the curve exactly replicate the whole curve at different scales. The construction of the Minkowski curve is based on a recursive procedure where at each step an 8-sided generator is applied to line segments, increasing the complexity. As the number of iterations increases, the length of the curve tends towards infinity, and its fractal dimension is calculated to be 1.5, demonstrating its self-similarity. Variations include starting with geometric shapes other than a straight line.