Metallica - the inside of a fractal - O2 etc...

**RobbeK** · 11-01-2014, 15:07

Hi all,

An attempt to do something with the inside of a fractal. (the difficult part).

A kind of Julia fractal is used (an extended) z(z+c)-c² , this is the formula to calculate the golden ratio (a/b=b/b+a).
The positive solution (1+sqrt(5))/2 is the most primitive contineous fraction possible [1,1,1 .... ] !!

The algorithm for the glow is logaritmic .
the reason is that iterations of f(z) deliver powers 2,4,8,16 , to get them perfectly smooth you will need something of the from log(log (....))

the orbit is calculated on abs(x*y) and this will define the glow- shape ... using the normal sqr(x²+y²) (the modulus) will generate circles and ellipses (i think ).
The glow formula can be turned into a function -- it will be dependant on the iteration level and the shape of the fractal (the more it goes to a circle the tougher ).

(this is not a copy from the web or so, it may be new )

best Rob

**Petr Schreiber** · 11-01-2014, 17:25

Hi Rob,

another fantastic demo, thanks for sharing!

Petr

**mike lobanovsky** · 11-01-2014, 18:09

Rob,

Your Metallica is very cool indeed! And you're right, I haven't yet seen anything similar in the way of fractal interior coloration yet so your approach looks very promising!

**RobbeK** · 11-01-2014, 21:28

Thanks ...

@Mike : attached the LogLog version (the way to go imho) -- I'll convert to plain Julia & then the Lord of the Rings.
(amazingly the inside is very conservative - code needs only a single run !! - all behave very similar )

@Petr : very much to discover here - I'm very curious to know if there's a correlation between the size of a non-choatic zone and how the orbit changes in that zone. (probably this will be another fractal structure ;-) Did you buy that Jupiter ??? any tests yet ??

best
Rob

(ah, yes if p.e. you turn the number of iterations into 36 (or so), you see it's fairly stable without changing any of the parameters in the algorithm)

**Petr Schreiber** · 11-01-2014, 23:18

Hi Rob,

one idea - maybe it would be good to make the iterations timer based, to keep the dialog responsive during the animation.

Regarding Jupiter - it was a big dilema, but I decided to save the money for now, as I discovered my father has 135mm f2.8 Nikon at home - so I would duplicate the "family gear" a bit with this purchase.

Petr

**mike lobanovsky** · 12-01-2014, 00:50

@Rob

I'm speechless! I'm frozen still and hypnotized out of my mind!

@Petr

It's not yet exactly what Rob is after.

Optimizations will come a little later and I'm dying to see his final results.

[EDIT] I've noticed that changing all Singles in the script to Doubles (O₂+TB) adds more pleasant relief to the picture. But can anybody explain to me why this also makes the script run noticeably slower for me? Is it too late in the evening here or are TB's Doubles slower to process than its Singles? I haven't seen anything in the O₂ sources that would make me think FPU precision may really matter there nor does it matter in FBSL...

**sblank** · 12-01-2014, 06:35

Very, very nice!

Stan

**peter** · 12-01-2014, 12:43

Hi,

I like this copper colour, looks great.

2012, I wrote these Mandels (in the zip file) it has a strong likeness somehow.
The Oxygen Dll is an ancient relict from the year 2011, but runs

I measure a time, but I can't remember what accurately I measure here.

**RobbeK** · 12-01-2014, 12:56

Thanks Peter , Stan (Peter, I'll have a look at them ).

Mike , Petr -- you both are correct ;-) the alfa3 hides the controls ...

changed :

bail out value from e to e²
!!! added a glow parameter -- this can be done by making the zone abs(ln(1)) wider , the value ln(ORB) changes from pos to neg here, generating the glow.
This done with the diffuse button (it is reset by StarT).
What'd you think ? better the more diffused ?

best Rob
(now a Mandelbrot map of this thing, and then upto Julia )

**mike lobanovsky** · 12-01-2014, 14:28

Rob,

Both versions look great but I don't yet know which one would be the best. Seems reasonable to keep both of them for later experimentation.

It seems to me the sharper glow version goes beyond the [255,255,255] limit at some places. There are occasional black dots seen at the crests from time to time, and I've even spotted momentarily a tiny green area. The upper limit of each component should be strictly clamped to 255.