【摘要】 目的研究相对论效应对分形维数的影响,为相对论分形几何学的建立奠定基础。方法从简单的均匀康托集入手,给出有相对运动时均匀康托集的维数计算公式,分析相对论效应对分形维数的影响。结果在运动系中观测均匀康托集时,其分形维数将变小。结论做相对运动的分形集,其分形结构将发生变化,因而分形维数必发生变化,从而为相对论分形几何学的建立奠定了基础,为改变分形维数提供了依据。更多还原

【Abstract】 Aim The relativistic fractal geometry will be founded based on the investigation of the fractal geometry when relativistic effect is considered.Methods The fractal dimension of uniform Cantor set is formulated in the case of regular moving.The influence of relativistic effect on the fractal dimension is researched in detail in this paper.Results The fractal dimension of uniform Cantor set will decrease when it is observed in a kinetic system.Conclusion The fractal dimension will change due to the variation of the fractal structure when relativistic effect is considered.It is useful to found the relativistic fractal geometry and extend the application of the fractal geometry.更多还原