END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

https://copy.com/d6ew4FTG2Gfk

An orbit plotted Nova, all orbits are plotted irrespective of whether the escape condition is met. Currently Saturn does not support rotation of orbit plotted fractals, so to get this image the custom dimensions of 500x750 pixels were employed and then expanded to 8000x12000 and the image was rotated to 12000x8000 using other software.

Titan Version 2.0 development

Parameters

Formula: Generalised Nova

z = transform(z)
z = z - alpha*(f(z)/f'(z)) + c
f(z) = z^beta - 1


alpha = 1 + 0i
beta = 3 + 0i

Programs: saturn and titan
Number of A transforms: 0
Number of B transforms: 0
Transform sequence: A
Number of Complex Plane transforms: 0
Initial values of z: 1 + 0i
Image centre: 0.828166666666666667 + 0i
Image width: 1.25
Rotation about image centre: 0 degrees
Maximum iterations: 3000
Bailout: norm(Δz) < 0.001
Calculation width: 3.75
Orbit length: 3000
Orbit plotting: all orbits
Colour method: sqrt

Note: this has been rotated 90 degrees.

Anti-Buddhabrot are boring... but now we know thanks to you that they can be interesting when the formula is modified   .

I beg to differ. The ordinary Mandelbrot set is "single formula, no parameters, and so on", but endlessly fascinating.

Mandelbrot have different colour methods, palletes (gradients) and so on. More interactive means more fun. Maybe this is reason why buddhabrot are less popular than super pictures it produces would suggest.

Here is a version plotting only captive orbits or at any rate orbits than haven't escaped by the time the maximum number of iterations has been calculated. This image is effectively the Anti-Buddhabrot Nova where as the first two images plot all orbits.


https://copy.com/4QDW0YKgKsK3

The software used to create these pictures is in a state of flux as I haven't nailed done the exact implementation of the colour methods, with this in mind, the plot using only escaped orbits has various grid like features that mar the image:


https://copy.com/3riLTYxfMHHy

I'm finding it much trickier getting decent images with just escaped orbits.

I can understand why orbit fractals aren't that popular zooming is a problem and they can also a VERY long time to calculate.

Actually, you could require points to settle to a periodic orbit to include them. Again the census would be incomplete, but you wouldn't have long-lived escapers in the mix.

Points that belong to the M-set, but not to its boundary, yes.

As for how long, it varies. There are iteration bands inside the circles and cardioids just like there are around the outside of the Set.