Title: Varying the power with each iteration Post by: matsoljare on July 03, 2010, 02:25:20 PM Has anyone tried making a Mandelbrot / Julia formula where the power increases with each iteration? That is, first iteration is power of 2, then 3, 4, 5 etc. I know there are formulas where the power alternates between two fixed values, but i'm not sure if this has been tried....
Title: Re: Varying the power with each iteration Post by: Sockratease on July 03, 2010, 02:53:41 PM I've done it with Mandelboxes and bulbs, but I usually take at least 100 frames to get the power from one value to the next. So the power per iteration would be something like 2.00, then 2.01, 2.02, etc.
In my opinion, integer leaps would be too abrupt to look good in an animation. Title: Re: Varying the power with each iteration Post by: Rathinagiri on July 03, 2010, 03:12:04 PM Hi Sockratease,
I think he mentions a different thing. Suppose, the iterations of a Mandelbulb be 30. He wants to render the Mandelbulb, first iteration at power 2, second at power 3, third at power 4 and so on. It is not about animation. In a single render image, the power increases as iteration increases. Title: Re: Varying the power with each iteration Post by: David Makin on July 03, 2010, 03:57:42 PM For standard 2D Mandelbrot/Jullia in Ultra Fractal:
Formulas: mmf.ufm:Transformation Mandelbrot/Julia Fractal type parameter "z^iter+c" Code: Fractal1 {Title: Re: Varying the power with each iteration Post by: Sockratease on July 03, 2010, 04:02:16 PM Hi Sockratease, I think he mentions a different thing. Suppose, the iterations of a Mandelbulb be 30. He wants to render the Mandelbulb, first iteration at power 2, second at power 3, third at power 4 and so on. It is not about animation. In a single render image, the power increases as iteration increases. Oh. Like this? (http://i106.photobucket.com/albums/m278/sockratease/2-7.jpg) That's a 6 formula bulb using powers 2 - 7 in order. Used Mandelbulb 3D. Interesting shape! I wonder what happens if the sequence of powers is varied... Maybe after my animation finishes rendering! Title: Re: Varying the power with each iteration Post by: David Makin on July 03, 2010, 04:03:36 PM Just to add that although the 2D ones aren't that interesting I think that both the 3D/4D Julibrot and the 3D Mandelbulb versions probably will be :)
Title: Re: Varying the power with each iteration Post by: David Makin on July 03, 2010, 04:04:55 PM Oh. Like this? That looks about right (though in my 2D formula the power on the 1st iteration is 1 rather than 2). Title: Re: Varying the power with each iteration Post by: Rathinagiri on July 03, 2010, 05:07:59 PM Nice one. In Mandelbulb 3D? How to do that?
Title: Re: Varying the power with each iteration Post by: Sockratease on July 03, 2010, 05:21:46 PM Nice one. In Mandelbulb 3D? How to do that? In Mandelbulb 3D there is a "Formulas" window for blending different formulas. Under Formula 1 I just put an "Amazing Bulb" and set the power to 2. Then under Formula 2, another Bulb set to power 3, and repeated (increasing the power by 1 for each new bulb) until I ran out of Formula tabs. I can upload a screen shot or an m3i file if you want. Title: Re: Varying the power with each iteration Post by: Rathinagiri on July 03, 2010, 05:37:45 PM Oh. Now I understand. Thanks for taking time to explain. :)
Title: Re: Varying the power with each iteration Post by: msltoe on July 03, 2010, 06:54:33 PM I've looked at this before for Mandelbulbs, series such as 2, 4, 8, 16, .... I called it "Fuzzy" because they get quite fuzzy...
http://www.fractalforums.com/theory/'fuzzy'-mandelbub/ (http://www.fractalforums.com/theory/'fuzzy'-mandelbub/) It's implemented in Mandelbulb 3D. Title: Re: Varying the power with each iteration Post by: Sockratease on July 03, 2010, 07:13:03 PM I've looked at this before for Mandelbulbs, series such as 2, 4, 8, 16, .... I called it "Fuzzy" because they get quite fuzzy... http://www.fractalforums.com/theory/'fuzzy'-mandelbub/ (http://www.fractalforums.com/theory/'fuzzy'-mandelbub/) It's implemented in Mandelbulb 3D. I love the Fuzzy formula! This was the first thing I did with my first version of Mandelbulb 3D (and it's a Fuzzy Formula) (it's a little off center, but I was just playing and learning the program - not making an effort at Fine Art!): (http://www.sockrateaze.com/stuff/1b1th.png) Bigger : http://www.sockrateaze.com/stuff/1b1.png Now... those who remember me know that I can't resist image editing my fractals. Especially when I think I can make something Silly happen!! So : (http://www.sockrateaze.com/stuff/1bth.png) Bigger : http://www.sockrateaze.com/stuff/1b.png Thanks for sharing this formula with us! Title: Re: Varying the power with each iteration Post by: Rathinagiri on July 03, 2010, 08:18:32 PM Very creative! |