Anyone have any questions about fractals?

Hello,

I am wondering if I can be of assistance to anyone that might have questions about fractals? I'm not quite an expert, but I do have about 10 years of experience playing around with them. Right now I'm focusing on quaternion-based fractals. I haven't had much experience with Mandelbulbs, but I'm always willing to learn.

I got my first print in the mail today (see attached image); it's a quaternion-based fractal printed out into plastic.



- Shawn

Nice.

Know of any software that is good for creating 3D fractals? How did you create this 3D model?

Thanks for the compliment. The fractals that I work with are called quaternion Julia sets.

QuasZ is a GUI fractal generator that supports export to 3D file formats (ie. OBJ, STL) . It's $30 --> https://www.mysticfractal.com/QuaSZ.html

Julia 4D 2 is a GUI fractal generator that supports export to OBJ. I wrote it about 10 years ago and it's cost-free and in the public domain. You may need to download a DirectX 9.0c runtime to run this app --> https://github.com/AnthonyNystrom/Julia-4D I've included a compiled version in a zip file attachment to this post.

I also wrote my own commandline fractal generator from scratch. It's cost-free and in the public domain and supports export to STL format. It's also GPU-accelerated, so it's much faster than the two other apps listed above --> https://code.google.com/p/qjs-isosurface/ I've included a compiled version in a zip file attachment to this post. You will need to download the GLUT and GLEW libraries to run this app.

I generated the model using my commandline software. The iterative equation that I used for this model is z' = sin(z) + c*sin(z). I use this equation to test which points along a 3D grid belong in the fractal set. Once those tests are complete, I use Marching Cubes to generate the final triangle mesh.

A really good introduction to quaternion fractals can be found at: https://paulbourke.net/fractals/quatjulia/

A really good introduction to Marching Cubes can be found at: https://paulbourke.net/geometry/polygonise/

A really good introduction to quaternion math can be found at: https://www.theworld.com/~sweetser/quaternions/intro/tools/to ols.html

If you're not into quaternions, a really good introduction to 2D fractals can be found at: https://www.codeproject.com/Articles/650821/Fractals-in-theor y-and-practice (see: Julia set).

Hope that answers your questions. If you'd like more detail on a certain part of my explanation, then please feel free to ask.

For the record, the model was printed using White Strong & Flexible plastic, and it's downright awesome to behold. Shapeways rocks!!!

Nice print!

I bet it would look awesome with some colour and done in Full Colour Sandstone.

I've been playing with Mandelbulb 3D (http://www.fractalforums.com/mandelbulb-3d/) recently - free software, with voxel stack capable output. I've not utilised the voxel output yet as I'm still learning the ropes with creating the actual 3D fractals.

Paul

I'm working on an x3d exporter right now. My aim is to make fractals with per-vertex colouring, similar to the screenshot I've attached.

Tada!

I've attached the C++ source code that converts an STL file into a rainbow-coloured X3D file.

I made another colouring scheme based on the vertex normal. It's included in the source code attached to my last post.

Perlin cow colouring.

Attached is a small tutorial on how to make quaternion Julia sets. Before jumping into quaternion Julia sets, it might be best to study the 2D Julia sets -- http://www.codeproject.com/Articles/650821/Fractals-in-theor y-and-practice