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Hi all, here's one based on bugman's latest suggestion, from here:

http://www.fractalforums.com/theory/3d-mandelbrot-formula-based-on-rotation-away-from-azimuthal-axis/ (http://www.fractalforums.com/theory/3d-mandelbrot-formula-based-on-rotation-away-from-azimuthal-axis/)

It's part of the z^8+c Mandelbrot.

"Theme Park Ride"

(http://fc07.deviantart.net/fs71/f/2009/344/c/f/Theme_Park_Ride_by_MakinMagic.jpg)

If no image above then look here:

http://makinmagic.deviantart.com/art/Theme-Park-Ride-146314193 (http://makinmagic.deviantart.com/art/Theme-Park-Ride-146314193)

Stunning.

I can sort of imagine pirate ships, roller coasters, log flumes, and other spinny rides being animated here!

very nice :D

Your colour choice really presents them in a nice way :)

On what are those colours based?

Also interesting shapes of course :)

Thanks :) The colours are just based on the idea that white, yellow and red is the sort of slightly gaudy combination often used on theme park and fair rides :)
I just realised that you possibly meant mathematically speaking ? In which case "solid" is based on a distance estimate minimum threshold value so the contours of the solid do not match the contours of iteration smoothing and that is what is used for the colouring look-up index (scaled).

so you basically colour it by a predefined gradient and the values to be used are the difference of true distance estimation and error?

Hmmm.... do you think, you could also try to color the set based on a spherical colour model?
(the center there is either black or white, so the brightness is either radius or inversed radius and the actual colour is given by the sign which gives the ratios of r,g,b...)

basically you start with colouring each point and then you just follow them without changing their specific colour... know what I mean?
So you could more or less graphically see where each point "came from" :)

Your current colouring technique is great too :)

> so you basically colour it by a predefined gradient and the values to be used are the difference of true distance estimation and error?

Not really "error", solid on smooth iteration and solid on distance estimate are two truly different methods so using one for "solid" and the other for colouring is not based on an error, just on two different calculations.

Colour by location is an option in the formula that I've not quite sorted yet :) I know it's very simple but I find it boring.

When I finally do the class-based versions of the formula you'll essentially be able to colour the object using any available UF colouring.

Thanks :)

This looks great! At first I didn't think this formula made very interesting looking Mandelbrots, but you've really added some nice flair to it.

I thought the same until I zoomed in :)
It seems this formula produces whipped cream but twisted in very interesting ways.