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Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature.  For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions.  Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature.  For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions.  Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

'''<font color="#ff8000"> 自组织临界性Self-organized criticality（SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，细胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的《生命的游戏》和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。

'''<font color="#ff8000"> 自组织临界性Self-organized criticality（SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，元胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的生命游戏和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。

{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。

{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。

== Examples of self-organized critical dynamics自组织临界动力学的例子 ==

== Examples of self-organized critical dynamics自组织临界动力学的例子 ==