Space Lotus

All Z=Z^2+C style fractals are essentially 4-dimensional with the 'C'onstant plane and the 'Z' plane, the planes having the C-real,C-imaginary and Z-real, Z-imaginary axis respectively. The typical 2D rendering you see of a fractal is viewing it only from the 'C' plane. If you rotate the data however you can view 4D fractals from different angles on different planes. That's what the well known Buddhabrot is (the Mandelbrot viewed from the 'Z' plane.)

I was curious about the structure of the Tricorn (aka Mandelbar). I had seen "Buddhabrot style" renderings of the Tricorn showing it from the Z-plane, but I have never seen it rotated. I decided to do rotate it around some of it's axis just to see what it's structure was like. I don't intend this to be a detailed tour like my "Under the Bodhi Tree" video, but there is an interesting zoom while rotating at the end.

After looking around this fractal I am really interested in doing a detailed tour of it once I get time to start on a new project.

This was rendered on my 2.16ghz Core2Duo Macbook using my own software. It was rendered at 1080x720 with 30 frames per second. Total render time was about 2.5 days.

Category:

Science & Technology

Tags:

• wmilberry
• Mandelbrot
• Fractal
• Mandelbar
• Tricorn
• math
• science
• 4D
• iterate
• animations

[dedly13]

can i ask which software package you used to make this?

[AluminumStudios]

@dedly13 I wrote my own code in C++ to generate this and my other fractal animations.

[MisterMikesh]

I love your animations! Are you going to publish your software sometime in the future?

[AluminumStudios]

@MisterMikesh Thanks for the comment.  My software is just something I did for myself. It's really not in a distributable state.

[dedly13]

@AluminumStudios thats pretty epic, may try some java stuff in that case :)

[harleyborgais]

That is so cool.

I wish very much to transmit this into the air and create a 3D light show.

These could replace the laser light shows, this would be far more awesome if holographically projected.

Could you figure out how to form this pattern, from 3D electrical waves, projected from two points?

[redbuttonstudio]

beautiful... 

[xlace]

Great animation. Nice synchronization with music and very good quality.