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(https://copy.com/d6ew4FTG2Gfk)
https://copy.com/d6ew4FTG2Gfk (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.

(https://copy.com/baYRrjANELmP)
https://copy.com/baYRrjANELmP (https://copy.com/baYRrjANELmP)

When I first implemented square root colouring for orbit plotted fractals there was a problem with the colour range being reduced as the image was expanded, this is what Orbit Plotted Nova should have looked like.

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

Boring is becouse single formula, no parameters and so on.

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

He replied to my "The Anti-Buddhabrot is boring".
And yeah I find the Original Anti Buddhabrot kinda boring.

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.

Even leaving that aside, it has all kinds of variety when zoomed deeply into.[/quote]


I think it's more that it's less interesting to zoom. It's more difficult and slow to zoom deeply into, and you tend to just see a few variations on the theme of "nebulae that resemble overlapping clusters of minibrots" without all the seahorse tails, etc.

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)
https://copy.com/4QDW0YKgKsK3 (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)
https://copy.com/3riLTYxfMHHy (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.

I like anti-buddhabrots, and yours is not a bad image!

Some antibuddhabrots appear sublime, lovely curves. An assemblage of water drops.

The problem with all antibuddhabots, however, is they're blasphemous. There's no way to separate impostor points -- long lived points - from points truly comprising the M-set. And the longer the dwell time the more the imposter points tarnish the image. With a buddhabrot there are no points from the M-set, though the census may be incomplete. Not as much of a problem, IMO

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.

Hmm, is it safe to assume points comprising the Mandelbrot set will settle into such an orbit? Perhaps for the majority of them, though not all.

And how long before they settle in such an orbit ;)

Don't think it's possible.

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.