"Pattern polymorphism of an imaginary shell"
gallery
"Pattern polymorphism of an imaginary shell"
Colour and pattern polymorphism refers to the occurrence of multiple discrete colour and pattern phenotypes within populations that result directly from genetic variation.In these following pictures, I am trying to explore colour and pattern on the surface of an imaginary shell through mathematical means.The platform I used was 3D-XplorMath-J.
Formula
- for the shape (same in all examples): x(u,v)=exp(w* u)*(h+a* cos(v)) *cos(s *u), y(u,v)=r *exp(w* u)*(h+a *cos(v))* sin(c* u), z(u,v)=exp(w *u)*(k+b *sin(v)), a=5.2, b=7, w=0.125, h=3.23, s=1, r=-1, c=1.016789, k=-16, Umin=-24, Umax=2, Vmin=0, Vmax=2pi. for the colour and pattern ( under the tab "user coloration RBG"): Red(u,v)=tan(2000u-v), Green(u,v)=v, Blue(u,v)=v.
Shell_1
Licence CC BY-NC-SA-3.0
Formula
- for the shape (same in all examples): x(u,v)=exp(w* u)*(h+a* cos(v)) *cos(s *u), y(u,v)=r *exp(w* u)*(h+a *cos(v))* sin(c* u), z(u,v)=exp(w *u)*(k+b *sin(v)), a=5.2, b=7, w=0.125, h=3.23, s=1, r=-1, c=1.016789, k=-16, Umin=-24, Umax=2, Vmin=0, Vmax=2pi. for the colour and pattern ( under the tab "user coloration RBG"): Red(u,v)=tan(1000u-v), Green(u,v)=v, Blue(u,v)=v.
Shell_2
Licence CC BY-NC-SA-3.0
Formula
- for the shape (same in all examples): x(u,v)=exp(w* u)*(h+a* cos(v)) *cos(s *u), y(u,v)=r *exp(w* u)*(h+a *cos(v))* sin(c* u), z(u,v)=exp(w *u)*(k+b *sin(v)), a=5.2, b=7, w=0.125, h=3.23, s=1, r=-1, c=1.016789, k=-16, Umin=-24, Umax=2, Vmin=0, Vmax=2pi. for the colour and pattern ( under the tab "user coloration RBG"): Red(u,v)=tan(23000u-v), Green(u,v)=v, Blue(u,v)=v.
Shell_3
Licence CC BY-NC-SA-3.0
Formula
- for the shape (same in all examples): x(u,v)=exp(w* u)*(h+a* cos(v)) *cos(s *u), y(u,v)=r *exp(w* u)*(h+a *cos(v))* sin(c* u), z(u,v)=exp(w *u)*(k+b *sin(v)), a=5.2, b=7, w=0.125, h=3.23, s=1, r=-1, c=1.016789, k=-16, Umin=-24, Umax=2, Vmin=0, Vmax=2pi. for the colour and pattern ( under the tab "user coloration RBG"): Red(u,v)=tan(40000-5v), Green(u,v)=v, Blue(u,v)=v.
Shell_4
Licence CC BY-NC-SA-3.0
Formula
- for the shape (same in all examples): x(u,v)=exp(w* u)*(h+a* cos(v)) *cos(s *u), y(u,v)=r *exp(w* u)*(h+a *cos(v))* sin(c* u), z(u,v)=exp(w *u)*(k+b* sin(v)), a=5.2, b=7, w=0.125, h=3.23, s=1, r=-1, c=1.016789, k=-16, Umin=-24, Umax=2, Vmin=0, Vmax=2pi. for the colour and pattern ( under the tab "user coloration RBG"): Red(u,v)=tan(40000u-5v), Green(u,v)=v, Blue(u,v)=v.
Shell_5
Licence CC BY-NC-SA-3.0
