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denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Wed Oct 16, 2013 7:41 pm    Post subject: 4D parametrics fonctions examples i post some parametrics examples in 4D , to illustrate the fonction. i start very simple with curves , because with one more dimention , the result will be planes in 3d 1 example the parabole cubique in 2D y=x^3 in 4D X = u Y = v Z = u^3 - 3*u*v^2 W = 3*u^2*v - v^3 With U[ -1, 1] And V[ -1, 1] what do you mind of that? cheers deniscLast edited by denisc on Fri Oct 18, 2013 10:59 pm; edited 1 time in total
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Fri Oct 18, 2013 6:41 pm    Post subject: hello all In my first post , i am inspired of this site; http://la-dimension4.com/Fonctions%20complexes.html if my first read, i am not understamd all. and now , a new curve sigmoide En mathématiques, la fonction sigmoïde (dite aussi courbe en S) est définie par : f(x)=1/1 + e^(- x) pour tout réel x\, mais on la généralise à toute fonction dont l'expression est : f(x)=1/1 + e^(-lambda* x) y=1/(1 +1/exp(x)) [x]: -8 , 8 [y]: -8 , 8 [z]: -0 , 0 ; and in 4D X = u Y = v Z = (exp(-u)* cos(v)+1)/(exp(-2 *u)* sin(v)^2+(exp(-u)* cos(v)+1)^2) W = exp(-u)* sin(v)/(exp(-2* u) *sin(v)^2+(exp(-u)* cos(v)+1)^2) U[ -pi, pi] V[ -pi, pi] another Courbe de Gauss y = exp(-x*x) in 4D X = u Y = v Z = exp(v^2-u^2)* cos(2 *u *v) W = -exp(v^2-u^2)* sin(2* u *v) U[ -1, 1] V[ -1, 1] for end Chaînette y = cosh(x)=exp(x)+exp(-x)/2 in 4D X = u Y = v Z = 1/2* exp(-u)* cos(v)+1/2* exp(u)* cos(v) W = 1/2* exp(u) *sin(v)-1/2* exp(-u)* sin(v) U[ -pi, pi] V[ -pi, pi] the probeme is , it's seem a same curve , but not same formula and calculs can a little bit different. more after cheers denisc
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Sat Oct 19, 2013 4:18 pm    Post subject: hello one more Cuspide cissoid of diocles You can see that on my site examples but less soution. y^2=x^3 4d: X=u*cos(v) ; Y=u*sin(v) ; Z=u^1.5*(cos(1.5*v) w=u^1.5*sin(1.5*v) and export in obj, make probleme i am plenty of v nan a+
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Thu Nov 07, 2013 10:56 pm    Post subject: hello all. now, a few example of 3D to 4d hopf in 3D X():cos(u)/2 Y():sin(u)/2 Z():(cos(u)*sin(v)-sin(u)*sin(v)*cos(v))/2 [u]:-pi, pi [v]:-pi, pi hopf in 4D X = cos(u)/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v))) Y = sin(u)/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v))) Z = (cos(u)*sin(v)-sin(u)*sin(v)*cos(v))/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v))) W = (cos(u)*sin(v)*cos(v)+sin(u)*sin(v)*cos(v))/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v))) With U[ -pi, pi] And V[ -pi, pi] cheers denisc
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Wed Dec 11, 2013 12:58 am    Post subject: intresting. still i have to say mandelbulb3d has more varied results:D
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Fri Dec 13, 2013 11:13 am    Post subject: hello uoface you can explain me a little, please? cheers denisc
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