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Oh. I 'm happy to share some formulas with the Forums, since I consider that you people are doing a very good work on the escapetime arena, and systems like the Quadray can generate very good fractals!

As for your spaceship (this is out of the thread, but.. ), its very good..
But let me melt it with my fully armed Incendia generated Space Cannon..
FIREEEE!!!!

indeed, i do not fully understand how incendia works, as far as i know it is using target regions, that somehow work like an IFS
but i never really understood what is the difference to standard IFS methods.....

Jesse rewrote the formula but why? It gives the same exact output as mine, and both ones don't look like Incendia's images, dunno why!

Small DEstop! The only thing that I didn't try

Effectively, your program is very sensible to thin surfaces; and it is not necessarily a defect, in some cases it reveals to be a great side-effect

So you included the derivative of the vectorlength, looks interesting.
My attempts of analytic DE's based on only one parameter were not good enough for 'power' bulb formulas, but this should be tested.



Max ray number?  Sounds like monte carlo or so  


Looks like you asking me, you are fully right, i use mostly the 4 point method.  Based on the escaped length gradient at same iterationcounts.

Would be also nice to get a little insight of Aexions rendering method, especially for this bulbs.


For this one i used the orbit trap to the origin, another implemented ones are smoothed iterations, last length increase and angles of escaped vector components, last ones are not very often used or useful.
There are far more possibilities, ask David for a wider summary, he has also much implemented in his UF formula file.

Its very good to see that the formula is finally implemented on M3D.
Well, hope to see some interesting renders.

About the questions:

I just writed a very basic raymarcher, nothing special (thats why I didn't saw the very fine tendrils). It outputs a buffer for Incendia and I made the final render from it.
(really a very crude process.. I have a lot to learn!)


Quadray coordinates are often overlooked but they produce very interesting results, in special for those higher dimensional objects. I have used them for years for plotting many interesting fractals (ifs attractors and sphere inversion fractals, for example:http://aexion.deviantart.com/art/Apollonian-Gasket-III-30135208). 

These links has some interesting quadray information:
http://minortriad.com/quadray.html
http://www.grunch.net/synergetics/quadintro.html

I will try to port some of the other 3D escape time fractals to the quadray, to see how they look..

Effectively *any* colouring that works for 2D fractals can be extended to colour the 3D surface - with the exception of DE if your surface threshold is based on DE or smooth iteration if your surface threshold is based on smooth iteration count and you can even use multiple "colourings" to say add bump-mapping or such.
Ideally said colourings would be proper 3D+ counterparts of the 2D ones e.g. orbit trapping to (a,b,c....) instead of just (a,b) but in order to allow more variety quickly my formula for UF allows you to specify a conversion of 3D values to 2D which can then be plugged into any of UF's (class based) complex colouring formulas.
Of course "any" is usually restricted to ones that work "Outside" (or "Inside") but not ones that work "Inside" only because generally the rendered surface is still mathematically "Outside" - that is unless of course you're rendering with "Inside" hollow and "Outside" solid in which case the reverse is true
For more IFS-style fractals you can also use the "genetics" for the colouring, in the case of KIFS or Mandelbox style fractals that means if you have say 3 conditionals per iteration each with 2 choices then you have 8 values per genetic "level" (iteration depth) and on doing the iteration for the surface pixel you can convert said genetic code to a colour in a manner of your own choosing. For instance with 8 values per iteration then at the end of each iteration loop I would use:

s = s/8 (divide size factor by 8, start value was 1)
code = code + newcode*s

Where newcode is 0 to 7 based on the path through the 3 conditionals.
Then use code for the colouring say as a simple index into palette/gradient (raw value of code here would be min 0 max<1).
Of course if there were say 12 possible routes through the iteration loop then newcode would be 0 to 11 and you'd divide s by 12 instead of 8.
Also you can make this a lot more complex giving the user finer control over the way the final code is created e.g. if there are 8 values from the loop but you only divide s by say 6 then the distribution of the colouring will be such that the variation between the primary fractal areas will be more graduated - though of course you lose the "ideal" range from 0 to <1 so you'd have to adjust accordingly.