net/web2/biomates */ draw2d( title = "All critical orbits for f(z)=z^5 +(0.8+0.4*i)*z^4 + z", terminal = svg, user_preamble = "set size square; set key...
z f = 1 / 4 {\displaystyle z_{f}=1/4} ( here big blue dot) then compute/draw orbits: critical orbit ( images of critical point = forward iteration of...
two vertical segments from critical point z=0 towards it's two preimages : a(z) = f^-1(z) and b(z) = -a(z). So it is: [a(z), -a] each (sub)segment of...
distance between last point of critical orbit and fixed point = ( cabs(zf) + cabs(z))/2 where z is the last point of critical orbit so in other words circle...
bifurcation points): r0: external ray 0 goes from (+) infinity along critical orbit towards critical point z=0 ( horizontal segment). Here bifurcates...
complex quadratic polynomial with fixed point z=0 and unique critical point z=-1/2 */ p(z):=z+z*z$ /* uy:f(ux) */ f(ux):= (a*ux + b ); /* only line segment...
end(); return 0; } setup start and end File 10000.8.pgm saved . Comment = Orbits File 10001.5.pgm saved . Comment = critical orbit t = 0.333333 z= -5000.000000...
= %f \n", cabs(z-z1)); /* forward orbit of critical point */ for (i=1;i<iMax ; ++i) { z = fc(z,C); printf("z = %f%+f \t |z-z1| = %f \n", creal(z), cimag(z)...
critical point z:0+0*%i */ orbit:[[realpart(z),imagpart(z)]], for i:1 thru iMax step 1 do ( z:expand(f(z,c)), orbit:endcons([realpart(z),imagpart(z)]...
z, int IterMax) { int i; // number of iteration for (i = 0; i < IterMax; ++i) { z = z*z*z*z*z*z +A*z+ c; // complex iteration z^6+A*z+c if (cabs (z)...
_=z^5_+(0.8+0.4)*z^4_+_z.svg){kind=link}
_=_z^2_+0.25.svg){kind=link}
_=_z*z_+_0.35.png){kind=link}
_=_z*z+0.25.svg){kind=link}
_=_z*z_+_0.35.svg){kind=link}
_=_z+a_2z_^2+O(z^3).svg){kind=link}
_=_z*z+c_where_c_=_-0.749998153581339_+0.001569040474910*I;_t_=_0.49975027919634618290_with_orbits.png){kind=link}
=_z^6+A*z+c_where_c_=_4.6875e-1_-_5.703125e-1_*I_and_A_=_6.96854889392852783203125e-2_-_1.07958018779754638671875e-1*I.png){kind=link}