Hello,
I was a bit under the impression (probably by looking at the depictions at Daniel's site) that tetration fractals are somewhat ugly. However as I now discovered and as I want to share with you thats absolutely not the case.
The following fractals are all generated with Fractal Explorer, the real/x axis is top-down, while the imaginary/y axis is left-right (picture symmetry just look better this way).
For the iterations we start with the value of the pixel as a complex number \( z_0 \) and then compute iteratively \( z=z_0^z \). If \( |z| \) gets over a certain threshold, then the number of iterations necessary for doing so is coded with colors. Black means it never gets over the threshold (at least not below the maximum of iterations performed).
Now have fun!
I start with the an overview picture:
The coordinate origine is roughly amidst the claws of the small lobster hanging down.
And \( e^{1/e} \) is roughly at the top of the middle stalagmite.
If someone wants to experiment for him/herself the fractalexplorer source file is attached.
I was a bit under the impression (probably by looking at the depictions at Daniel's site) that tetration fractals are somewhat ugly. However as I now discovered and as I want to share with you thats absolutely not the case.
The following fractals are all generated with Fractal Explorer, the real/x axis is top-down, while the imaginary/y axis is left-right (picture symmetry just look better this way).
For the iterations we start with the value of the pixel as a complex number \( z_0 \) and then compute iteratively \( z=z_0^z \). If \( |z| \) gets over a certain threshold, then the number of iterations necessary for doing so is coded with colors. Black means it never gets over the threshold (at least not below the maximum of iterations performed).
Now have fun!
I start with the an overview picture:
The coordinate origine is roughly amidst the claws of the small lobster hanging down.
And \( e^{1/e} \) is roughly at the top of the middle stalagmite.
If someone wants to experiment for him/herself the fractalexplorer source file is attached.