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+---
+title: Iteration and chaos
+description: A brief introduction to iteration and chaos
+date: 2024-05-26T14:18
+update: 2024-05-26T23:04
+tags:
+  - wiki/mathematics
+  - wiki/complex-system
+  - wiki/computational-physics
+id: wiki20240526141811
+dg-publish: true
+maturity: sapling
+---
+# Iterative methods for computing physical quantities
+
+If a physical quantity is involved in the expression of itself :
+$$
+f(x)=x \tag{1-1}
+$$
+Iterative methods are usually employed for solving it.
+
+## Direct iterative method
+
+Let $f(x_n)=x_{n+1}$，compute from a preset $x_0$ until $x_n=x_{n+1}$.
+
+Considering the limited iterative steps in real world, a strict equation is hard to get. Usually, a convergence factor $\epsilon$ is used for qualification:
+
+$$
+\bigg | \frac{x_{n+1}-x_n}{x_n} \bigg | \leq \epsilon
+$$
+## Newton iterative method
+
+to be continued...
+# Chaos and fractal