Cross Product Mandelbrot

[kram1032]

Just an other thought: Try random starting values (but save them, just in case you find something interesting )

[makc]

Just an other thought: Try random starting values (but save them, just in case you find something interesting )

if you mean R1s I think it is now quite obvious that we'd only get same thing rotated to new direction.

[MTd2]

Hmm. I feel ignored here...

Try to do a cross section of the ovoid... and later try the 2nd formula...

[makc]

Try to do a cross section...

I can't because my program only does 3D but still what would you expect to see there? It will be circle (or ellipse) with two optional rays.

[MTd2]

Try to do a cross section...

I can't because my program only does 3D but still what would you expect to see there? It will be circle (or ellipse) with two optional rays.

It could be a swiss cheese! You have to open it to see what's inside. And, if it doesn't work, could you try the 2nd formula I posted, pleaaaaaaase!

BTW, how do you do 3d?

[makc]

how do you do 3d?

pretty straightforward, for every pixel you make a ray going from your eye through that pixel, and then iterate 3d points along that ray until you have convergence.

[MTd2]

Hmm, it is not difficult to take a cross section

Take R1=(0,0,1) amd R0=(0,y,z) and plot y,z. The x will just matter in the calculations.

[makc]

It could be a swiss cheese!

I added x - y + 1.5*z > 0 condition, and... no cheese for you:

And, if it doesn't work, could you try the 2nd formula I posted, pleaaaaaaase!

That looks pretty similar to what I had before, just this time the curving is a "feature", not a bug:

[MTd2]

Damn it...

What if then:

R_n+1 <- R_nX{R_n*M}+R₀

where M is a matrix that rotates Rn

The first term makes a kind of square of the vector, a "cross vector square" in analogy to the mandelbrot case.

[makc]

What if...

I think we all can make a blind guess, but is there anything that makes you think yours will have some interesting features?

[MTd2]

It is more  than having interesting features. I want to see if it is possible to make fractals like the ones of mandelbrot by iterating surfaces. For exmple, the cross vector determines the generator of a surface. It would be a first step for creating fractals based on real physics. For example, the vector product between the differential operator and the electric or magnetic field induces each other. So, maybe one day we could get electro magnetic fractals, standard model fractals, quantum gravity fractals.

So, I am trying to find a very primitve way to generate a fractal by iterating surfaces.

[makc]

...For example, the vector product between the differential operator and the electric or magnetic field induces each other. So, maybe one day we could get electro magnetic fractals...

I would start looking here:

<a href="http://www.youtube.com/v/OsW8zctD7CM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/OsW8zctD7CM&rel=1&fs=1&hd=1</a>

btw I have no clue what "iterating surfaces" is

[MTd2]

I know that video. That is awesome, but I'd like really a fractal.

BTW, Don't you iterate points of the complex plane? So, why not little pieces of surfaces? A surface is determined by a vector perpendicular to that surface, but that vector is also proportional to the cross product of the tangents of that surface.

So, you see, you have an output, the vector that specifies that surface, and 2 inputs, the tangents. If you say that one of these inputs determine other surface, than you can determine an infinite recursion.
 

[makc]

this is about the same level of logic as saying whenever calculations involve n numbers we are dealing with n-dimensional vector it is nice to pretend it sometimes but never the less these could be just n unrelated numbers.

[MTd2]

Well, you showed me an example of a fractal that involves vectors:http://en.wikipedia.org/wiki/The_vector_of_a_quaternion#Vector

But I am talking about vectors that generates surfaces, thus the cross prodcut. I am not interested here in scalars, as in the case you showed.