Chaotic Image---Enontekiö owl

Professor Enontekiö (M.henon) of the Nice Observatory in France proposed a number of two-dimensional mappings in the study of celestial mechanics, usually in the Ethiopian mapping H:

X_ (n+1) =1-ax^2_n+y_n

Y_ (n+1) =bx_n

Where A and B are parameters, when |b|<1, H is dissipative, and when | b|=1, H is conservative. This mapping is Enontekiö in 1976, the study of more people, almost every chaotic book to mention, of which Professor Huangyongnio of the Department of Mechanics of Peking University uses pure Algebra method to study Enontekiö mapping, very unique.
Then Enontekiö, in 1969, proposed a conservative mapping in the form of G:

X_ (n+1) =x_ncost-y_nsint+x^2_nsin T,

Y_ (n+1) =x_nsint+y_ncost-x^2_ncos T,

Astronomers, this is a very high profession. Remember that is the primary school age, a lot of students ideal.

This generates a chaotic image using the script code of its own definition syntax. Related software see: Ychaos generating chaotic images. If you are interested in a graphic image of students, welcome to join QQ Group: 367752815

[1]

[Scriptlines]t=11.4*x*x + yy=0.3*xx=t[variables]x =0.000000y=0.000000

The image is too general.

[2]

Change the parameters to see:

[Scriptlines]u=1 -a*x*x + b*yv=x- yx=Uy=v[variables]a=  0.186500b=-0.985000x=0.010000y=0.010000

Stronger than the first.

[3]

Add some more changes.

[Scriptlines]u=1-A*x*x + b*YV=x-yl=SQRT (U*u + v*v) U=if(l<0.01, u/0.01, u) v=if(l<0.01, v/0.01, v) x=x+Uy=y+VL=SQRT (x*x + y*y) L=mod (L,1.5)/LX=if(l<1, x*l,x) y=if(l<1, y*l,y) [Variables]a=1.280000b=-0.985000x=0.010000y=0.010000

[4]

Add random perturbation

[Scriptlines]u=1-A*x*x + b*YV=x-yl=SQRT (U*u + v*v) U=if(l<0.01, u/0.01, u) v=if(l<0.01, v/0.01, v) x=x+Uy=y+VL=SQRT (x*x + y*y) L=mod (L,1.5)/LX=if(l<1, x*l,x) + rand2 (-r,r) y=if(l<1, y*l,y) [Variables]a=1.280000b=-0.985000R=0.001000x=0.010000y=0.010000

[5]

Look at the G formula again:

[scriptlines]b=sin (a) c=cos (a) t=x*c-y*b + x*x*by =x*b + y*c-x*x*cx= t[variables]a=3.000000x=1.000000y=1.000000

A big circle.

[6]

Change it:

[scriptlines]b=sin (a) c=cos (a) t=x*c-y*b + x*x*by =x*b + y*c-x*x*CX4  ) y=mod (y,4) [Variables]a=3.678000x=1.000000  Y=1.000000

It's like an owl.

[7]

Final version:

[scriptlines]b=sin (a) c=cos (a) t=x*c-y*b + x*x*by =x*b + y*c-x*x*CX4 ) + rand2 (-r,r) y=mod (y,4) + rand2 (-r,r) [Variables]a=3.647602r= 0.001000 x=1.000000y=1.000000

Chaotic Image---Enontekiö owl