Breather surface of mathematical graphics

This is a pretty curved surface, but I have not found many explanations.

In differential equations,Breather SurfaceIs a mathematical surface relating to breathers.

The mathematical formula is complex. The parameter equation is:

Where 0 <A<1.

Wikipedia related URLs: http://en.wikipedia.org/wiki/Breather_surface

Use the script code of your own defined syntax to generate mathematical graphics. For more information about the software, see: Mathematical graphics visualization tool. This software is free and open source. QQ chat group: 367752815

#http://xahlee.info/surface/breather_p/breather_p.htmlvertices = D1:100 D2:100u = from -13.2 to 13.2 D1v = from -37.4 to 37.4 D2b = 0.4r = 1 - b*bw = sqrt(r)d = b*((w*cosh[b*u])^2 + (b*sin[w*v])^2)y = -u + (2*r*cosh[b*u]*sinh[b*u])/dz = (2*w*cosh[b*u]*(-(w*cos[v]*cos[w*v]) - sin[v]*sin[w*v]))/dx = (2*w*cosh[b*u]*(-(w*sin[v]*cos[w*v]) + cos[v]*sin[w*v]))/d

 

Use random number

#http://en.wikipedia.org/wiki/Breather_surfacevertices = D1:100 D2:100u = from -13.2 to 13.2 D1v = from -37.4 to 37.4 D2a = rand2(0.1, 0.9)w = sqrt(1 - a*a)d = a*((w*cosh[a*u])^2 + (a*sin[w*v])^2)y = -u + (2*(1 - a*a)*cosh[a*u]*sinh[a*u])/dz = (2*w*cosh[a*u]*(-(w*cos[v]*cos[w*v]) - sin[v]*sin[w*v]))/dx = (2*w*cosh[a*u]*(-(w*sin[v]*cos[w*v]) + cos[v]*sin[w*v]))/d