Are fractals and chaos synonymous?
No. Many people do confuse the two domains because, regularly, books or papers about chaos either speak of the two concepts or are illustrated with fractals. Fractals and deterministic chaos are mathematical tools to model different kinds of natural phenomena or objects. The keywords in chaos are non linear, unpredictability, sensitivity to initial conditions in spite of the deterministic set of equations describing the phenomenon. On the other hand, the keywords for fractals are self-similarity, invariance of scale. Many fractals are in no way chaotic (Sierpinsky triangle, Koch curve…). However, starting from very different points of view, the two domains have many things in common: many chaotic phenomena exhibit fractal structures (in strange attractors, for example; fractal structure is also obvious in chaotic phenomena due to successive bifurcations such as the logistic equation).
