Newton Fractals

Following in Reptorian’s footsteps, I became interested in Newton fractal yesterday, and tried to implement it in G’MIC.
Today, I’ve released a new filter for the G’MIC-Qt plug-in, that can be found in Rendering / Newton Fractal. Here are some screenshots of this filter in action:

The differences with the version from Reptorian, is that I’ve tried to make this filter the most generic possible :

  • Users can write their own math expressions for rendering the fractal.
  • Coloring of the rendered image can be done with three different methods, one being a Custom coloring mode, where the user can write the math expressions he wants to display the fractal variables as a new image.
  • There is a ‘almost-interactive’ navigation system which eases the navigation in the complex plane. This has been borrowed from my previous Mandelbrot filter, and while it’s not perfect, it’s quite usable, considering the current limitations we have with the plug-in interface. It may be improved in the future though.

I’m quite happy with how this filter behaves right now. There is always room for improvements of course, but that’s a good beginning.

Here are a few images I’ve obtained with this filter so far, do not hesitate to share your own images!

newton_ex1

newton_ex2

newton_ex3

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Wow, that’s something to try testing. I think I might look into this filter for how I can improve the Thorn Fractal filter.


EDIT: I have decided to test your filter. Here’s my result:

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That’s beautiful.
I’m working on some improvements right now, to speed up preview computation (by subsampling).
I’ll probably allow to specify a rotation angle as well.
Stay tuned :slight_smile:

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Really beautiful fractals.
Reptorian, David, is it posssible to superposition formulas of flame and Thorn fractals with Newton’s to get some new fractals ?

Or combine them with juxtaposed iterations with one another?

By mixing formulas, theoretically possible, but it’s a lot of work for both of us. I would be open to collaborating on that, but as of now, no.

I don’t know what kind of fractal is this. Can this be done with formula ?

Found with Google:

https://dianaquintero-uts.blogspot.com/2014/09/blog-post.html?m=1 and
https://www.grasshopper3d.com/profile/DianaQuinterodesaul

This is a procedural 3d model, made by Diana Quintero. Probably with Grasshopper 3D for Rhino.

So…, I think this can’t be done in G’MIC.

But if you are interested in procedural 3d modeling with FOSS, then you can use Blender and Sverchok:

http://nikitron.cc.ua/sverchok_en.html

and Sorcar:

And if you want animate this kind of things, you can use Animation Nodes:

Jimmy Gunawan has a YouTube channel with hundreds of videos with examples of this software:

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On the contrary, I think it’s possible to do it in G’MIC. The problem is more about who want to do it ?
:stuck_out_tongue:

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Is it possible to use reqursive quadtree variations with rep_thorn_fractal, Newtons fractals to get new patterns?

No.

The potential issue is that Rhino is based on NURBS paragism, and Blender lacks proper NURBS support. Polygon and subdivision will always lack the surface quality of NURBS(This is one reason why Blender and Maya and so on will never replace NURBS-based software). It’s probably not possible in Blender.

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Reptorian, that image reminded me on your thorn fractals but wrapped around and twisted.

Before we get back on topic, I should remind you that you may benefit from learning mathematics and coding, then your dream may or may not be true.