Bifurcation of Boundary Wavefronts for Some Graphs

initial front

2

x

3

x

4

x

-x+

3

x

-

3

x

+

5

x

Sin[x]

3

Sin[x]

x



-Log[x]

enable boundary

boundary point

time

This Demonstration shows bifurcations of wavefronts generated by some curves with and without boundaries (red points). Wavefronts are generated by a curve and its normal boundary. We are concerned with local bifurcations on initial wavefronts around a point as a function of time, that is, behavior of the shape of a wavefront around a red point at times when the shape has a singularity.