- #1
coolnessitself
- 35
- 0
I'm working on a visualizer of sorts for a system:
[tex]
x_{n+1} = sin(a y_n) - cos(b x_n)[/tex]
[tex]
y_{n+1} = sin(c x_n) - cos(d y_n)
[/tex]
with [tex]a,b,c,d \in [-2.5, 2.5][/tex]
So for whatever initial [tex](x_0,y_0)[/tex] I give the system, I know the next iteration will have both x and y between -2 and 2, and that will be true for all n>0.
However, for certain values of a,b,c,d, you could say that all [tex]x_{n>0}[/tex] and [tex]y_{n>0}[/tex] will be within some other, possibly smaller, area. How can I find these dimensions given a,b,c,d?
(I'll use this to scale the area on which the plot is drawn, so for those values of a,b,c,d which result in a small area, the plot will fill the entire space)
[tex]
x_{n+1} = sin(a y_n) - cos(b x_n)[/tex]
[tex]
y_{n+1} = sin(c x_n) - cos(d y_n)
[/tex]
with [tex]a,b,c,d \in [-2.5, 2.5][/tex]
So for whatever initial [tex](x_0,y_0)[/tex] I give the system, I know the next iteration will have both x and y between -2 and 2, and that will be true for all n>0.
However, for certain values of a,b,c,d, you could say that all [tex]x_{n>0}[/tex] and [tex]y_{n>0}[/tex] will be within some other, possibly smaller, area. How can I find these dimensions given a,b,c,d?
(I'll use this to scale the area on which the plot is drawn, so for those values of a,b,c,d which result in a small area, the plot will fill the entire space)