Simon Snake's 86f formula plugin available

[panzerboy]

http://www.fractalforums.com/new-theories-and-research/is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-2d/msg57801/#new

Plugin for Simon's Formula is available here...
http://sourceforge.net/projects/simon86f/files/

A quick demo

<a href="http://www.youtube.com/v/BfkfkebcjEs&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/BfkfkebcjEs&rel=1&fs=1&hd=1</a>

[simon.snake]

All I can say is wow, breathtaking.

Many thanks.

[Dinkydau]

Nice vid

I downloaded the formula. I find it very interesting that from a distance it looks like a power 6 mandelbrot set, while zoomed it it looks like a power 4 mandelbrot set.

It gives only black pixels when an iteration count over 16200 is used for some reason.

[panzerboy]

I've updated the files on Sourceforge.
I had some logic for smooth shading that was still active for the non-smoothed formulae.
It was probably causing the 'feature' Dinkydau discovered with things going black once the iterations got to 16200 (probably 16384?).

[simon.snake]

Thanks Panzer.

I'm not sure but is there something slightly off with the smooth shading?  There seems to be a slight banding on the colours.

[panzerboy]

Oh yeah, big time.
I haven't been able to get the smooth shading matched well.
There are the occasional iterations with random fuzz through them, don't know what causes that.
Previous formulae have had that effect solved by preserving more integer bits in the calculations.
That is trading off decimal precision to allow for larger numbers.
That makes things better but doesn't solve the problem.
Then there's the mapping, the Smooth shading algorithm I'm using is for mandelbrot which squares the z.
That does a log(log(sqrt(zisqr+zrsqr)))-log(log(OverFlowPoint*OverFlowPoint))
For all the extra arithmetic of your formula that might now need to be somthing like...
log(log(sqrt(log(log(sqrt(log(log(sqrt(zisqr+zrsqr)))))))-log(logt(log(log(OverFlowPoint*OverFlowPoint))*log(log(OverFlowPoint*OverFlowPoint))))*log(logt(log(log(OverFlowPoint*OverFlowPoint))*log(log(OverFlowPoint*OverFlowPoint))))
perhaps?
I have some experimenting to do.

[simon.snake]

Well, that's complicated!

Certainly not for the faint hearted.

All those logs would slow it down quite a bit further.

I didn't realise you had to do a whole bunch of additional maths to implement it.

[Dinkydau]

I've updated the files on Sourceforge.
I had some logic for smooth shading that was still active for the non-smoothed formulae.
It was probably causing the 'feature' Dinkydau discovered with things going black once the iterations got to 16200 (probably 16384?).

Yes I had noticed it in the meantime. Increasing iterations A LOT makes stuff visible again. The blackness really started from 16200 on instead of 16384.