The Strange Attractors of Gumowski-Mira
Authors' Data: Housam Binous, Asma Hélaoui 
and Asma Chaghal
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Reference :
http://math.cmaisonneuve.qc.ca/alevesque/chaos_fract/Attracteurs/Attracteurs.html

Strange attractors found by Gumowski-Mira have shapes that reminds marine life.

f[x_]:=A x+2 (1-A) x^2/(1+x^2)

x[0]=3;y[0]=1;

i=0;

A=-0.31;B=1;

While[i<10000,x[i+1]=B y[i]+f[x[i]];
y[i+1]=-x[i]+f[x[i+1]];i=i+1]

i=0;

tbl=.

While[i<10000,tbl[i]=Table[{x[j],y[j]},{j,i,i+1000}];i=i+1000];

i=0;

While[i<10000,plt[i]=ListPlot[tbl[i],PlotStyle->Hue[i/10000],DisplayFunction-> Identity];i=i+1000]

Show[Flatten[Table[plt[i],{i,0,9000,1000}]],DisplayFunction-> $DisplayFunction]

x[0]=0.8;y[0]=0.4;

i=0;

A=-0.23;B=1;

While[i<10000,x[i+1]=B y[i]+f[x[i]];
y[i+1]=-x[i]+f[x[i+1]];i=i+1]

i=0;

tbl=.

While[i<10000,tbl[i]=Table[{x[j],y[j]},{j,i,i+1000}];i=i+1000];

i=0;

While[i<10000,plt[i]=ListPlot[tbl[i],PlotStyle->Hue[i/10000],DisplayFunction-> Identity];i=i+1000]

Show[Flatten[Table[plt[i],{i,0,9000,1000}]],DisplayFunction-> $DisplayFunction]

x[0]=3;y[0]=1;

i=0;

A=0.31;B=1;

While[i<10000,x[i+1]=B y[i]+f[x[i]];
y[i+1]=-x[i]+f[x[i+1]];i=i+1]

i=0;

tbl=.

While[i<10000,tbl[i]=Table[{x[j],y[j]},{j,i,i+1000}];i=i+1000];

i=0;

While[i<10000,plt[i]=ListPlot[tbl[i],PlotStyle->Hue[i/10000],DisplayFunction-> Identity];i=i+1000]

Show[Flatten[Table[plt[i],{i,0,9000,1000}]],DisplayFunction-> $DisplayFunction]

x[0]=3;y[0]=1;

i=0;

A=-0.77;B=.95;

While[i<10000,x[i+1]=B y[i]+f[x[i]];
y[i+1]=-x[i]+f[x[i+1]];i=i+1]

i=0;

tbl=.

While[i<10000,tbl[i]=Table[{x[j],y[j]},{j,i,i+1000}];i=i+1000];

i=0;

While[i<10000,plt[i]=ListPlot[tbl[i],PlotStyle->Hue[i/10000],DisplayFunction-> Identity];i=i+1000]

Show[Flatten[Table[plt[i],{i,0,9000,1000}]],DisplayFunction-> $DisplayFunction]