Analysis On Koch Curves

After fractal introduced by Mandelbrot, people mainly study some staticproperties of fractal, such as measures and dimensions of fractals. But, in order to explainsome physical phenomena, people should study the dynamical properties of fractals and definethe Laplace operator on the fractals. Through the eforts of mathematicians some self-similarenergies on finitely ramified fractals are constructed.In the paper, by discussing energy of graph and Lagrangian energy on Koch curve and itsdeformations (Koch curve with random orientation and Koch curve with random interval), weobtain that energy of graph has nothing to do with their shape, dimension, and bifurcation,however, Lagrangian energy has connection with their shape, dimension and bifurcation.