08/19/2015, 03:28 PM

In analog to mandelbrot fractals let our starting values be x_0,x_1.

Let p1,p2 be polynomials of degree 2 or 3.

Now we define the recursion

X_n = p1(x_{n-1}) + p2(x_{n-2})

Now let x_0,x_1 be simple functions of z.

To keep it simple say x_0 = 0 , x_1 = z.

Then color the plane according to

Lim n -> oo

X_oo(z)

In case of divergeance use black.

(Or larger then say 10^131 after Some steps)

This should give Nice pictures i assume.

Does it look like a fractal in most cases ?

If it does not look like a fractal, what does it look like ?

Some pictures are appreciated.

Regards

Tommy1729

Let p1,p2 be polynomials of degree 2 or 3.

Now we define the recursion

X_n = p1(x_{n-1}) + p2(x_{n-2})

Now let x_0,x_1 be simple functions of z.

To keep it simple say x_0 = 0 , x_1 = z.

Then color the plane according to

Lim n -> oo

X_oo(z)

In case of divergeance use black.

(Or larger then say 10^131 after Some steps)

This should give Nice pictures i assume.

Does it look like a fractal in most cases ?

If it does not look like a fractal, what does it look like ?

Some pictures are appreciated.

Regards

Tommy1729