WOLFRAM|DEMONSTRATIONS PROJECT

Typical Bifurcations of Wavefront Intersections

​
2D
1
0
(
0
A
1
A
1
​
1
0
(
0
A
1
A
2
​
1
0
(
0
A
1
B
2
​
1
0
(
0
A
1
0
A
1
A
1
​
3D
1
0
(
0
A
1
A
1
​​(+)
1
0
(
0
A
1
A
1
​​(-)
1
0
(
0
A
1
A
2
​​(+)
1
0
(
0
A
1
A
2
​​(-)
1
0
(
0
A
1
A
3
​
1
0
(
0
A
2
A
2
​​(+)
1
0
(
0
A
2
A
2
​​(-)
1
0
(
0
A
1
B
2
​​(+)
1
0
(
0
A
1
B
2
​​(-)
1
0
(
0
A
1
B
3
​
1
0
(
0
A
1
+
C
3
​
1
0
(
0
A
1
-
C
3
​
1
0
(
0
B
2
B
2
​​(+)
1
0
(
0
B
2
B
2
​​(-)
1
0
(
0
A
1
0
A
1
A
1
​
1
0
(
0
A
1
0
A
1
A
2
​
1
0
(
0
A
1
0
A
1
B
2
​
1
​​
0
0
A
1
0
A
1
0
A
1
A
1
​
time
This Demonstration shows all generic bifurcations of
m
intersections of wavefronts generated by a hypersurface with or without a boundary in a smooth
n
-dimensional manifold for
m≥2
,
n≤3
. The time can be varied with a slider.