sjenkin1

For all the below functions, iterate each 7 times, from $x_0

=1$

Number 1 is right off the Quiz 1 review sheet.

1) $f(x)=x^2 -1$

2) $f(x)=2x^2-2$

3) $f(x)=x^3+3$

4) $f(x)= (x^2)/2$

An archived instance of discourse for discussion in a Fractal Introductory Colloquium.

sjenkin1

For all the below functions, iterate each 7 times, from $x_0

=1$

Number 1 is right off the Quiz 1 review sheet.

1) $f(x)=x^2 -1$

2) $f(x)=2x^2-2$

3) $f(x)=x^3+3$

4) $f(x)= (x^2)/2$

mark

Crazy - where'd you get these???

sjenkin1

Off the top of my head.

Chief_Keith

- -1,0,-1,0,-1,0,-1
- -2,6,70,9798,192001606,7.37*10^16,1.09*10^34
- 3,30,27003, many big numbers
- 0,0,0,0,0,0,0

sjenkin1

I don't think number 4 iterates to 0 over and over.

Chief_Keith

Yes it does, because $$0^2 = 0$$ and $$0/2 = 0$$thus having the same output as the input, which results in the same number every time. Did I do my math wrong on something?

mark

@Chief_Keith You are correct that $0$ is a fixed point, *but* the problem states that $x_0=1$.