Title: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 20, 2012, 03:51:38 AM The idea of the tanglebrot is that when you are near the root regions of the Mandelbrot (in this case the Juliabrot), permute the coordinates and scale the coordinates. The formulation I've come up to make it somewhat nice looking is a bit of a hack.
Maybe we can find better parameters and/or formulas to work with. Here's the inner loop: r=x*x+y*y-z*z; if (r>0.01) { x1 = (x*x-y*y); y1 = 2*x*y; z1 = -2*z*sqrt(x*x+y*y+0.5*z*z); x = x1+a; y = y1+b; z = z1+c; } else { x1=z*3; y1=x*3; z1=y*3; x=x1;y=y1;z=z1; } (http://nocache-nocookies.digitalgott.com/gallery/12/803_20_10_12_3_42_34.png) Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 20, 2012, 04:37:45 AM Another J-set that is a little easier to visualize what's going on:
(http://farm9.staticflickr.com/8050/8104271916_f451d61f0f_b.jpg) Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: matsoljare on October 20, 2012, 03:51:27 PM Can you try this on a Julibrot?
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 20, 2012, 05:24:42 PM Matsoljare, thanks for the request. I think you mean the M-set. The above two were J-brots.
Here's the M-set, not nearly as convincing. Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: matsoljare on October 21, 2012, 09:23:35 PM Yeah, sure isn't convincing at all.... cause it only shows an error message!
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 21, 2012, 09:52:52 PM The M-set picture was in my Flickr photostream. I modified the post and put the image on the forum.
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: cKleinhuis on October 21, 2012, 10:07:48 PM it is loking nice, a candidate, not much detail, but certainly a candidate containing the mset ... so lets see how the 8th power looks ;)
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: DarkBeam on October 22, 2012, 12:12:01 PM Lil question;
Is the formula discontinue? :dink: Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: matsoljare on October 22, 2012, 11:37:57 PM Wow, that looks awesome, i'd like to see some closeups, on the middle of the main bulb especially....
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 23, 2012, 04:10:11 AM Thanks guys!
DarkBeam: The formula I've presented is discontinuous, although the breaks are not to so jarring because they occur only when the permutation is made and there is often space between the two segments. I'm working on a C0 continuous version, but I'm not sure if it will pan out. Christian: Not sure what an 8-th order would mean for this beast given I'm not using a typical spherical coordinate-derived formula. My goal has always been to get the 2nd order to have lots of fractal goodness. I think that when we go up to 8th order with a lot of these functions we get lots of near-conformal regions to feast our eyes on. Matsoljare: Here's a closeup of the center of the M-set. Looks like navel lint to me: :) Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: KRAFTWERK on October 23, 2012, 08:44:05 AM Those Julias are beautiful :beer:
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: Alef on October 23, 2012, 05:18:54 PM cutted julia features is nice and used colour method is nice. But probably old formula revisited Bennesi looks more grailish;)
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: msltoe on October 24, 2012, 02:19:39 AM One more J-set to put out there. I made the formula more continuous if anyone is interested I'll post the formula.
I call this one "Dragons": Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: Alef on October 28, 2012, 05:01:53 PM Discontiniues looks better. Anyway, probably there are smooth surfaces of discontiniuaties, and not mess like Barnsley formula. At least it don't seems mess like Barnsley. Maybe this could be a transform. Like most 3D brots it is fractal in 2 dimensions, just it is more beautifull. :peacock:
Title: Re: Introducing the Tanglebrot: Another valiant attempt at the holy grail Post by: DarkBeam on January 30, 2015, 10:48:38 AM Ack! Please yes post the continuous version? :D |