Fractal Images or Videos

Typoz made me realise that fractals don't show their true beauty until they are animated!

Typoz's Fractal 2 contains sequences which look extraordinarily close to what you see if you watch a supersaturated solution suddenly crystalize.

Yes, that second one is just a very ordinary Mandelbrot rendering. One of the things which is obvious when starting to zoom in is that a lot of areas look black or empty until the (upper limit on the) number of iterations is increased. I'm sure it's not an original idea, I came upon my own idea for changing the number of iterations very gradually. Start with too high a figure and the image is filled with fine detail which actually hides rather than reveals what is there. So it starts off with a few hundred iterations per frame, ends with a few thousand.

My aim was to keep a certain amount of black there, it is like the sky against which a tree can be seen, whereas a tree in a forest is less visible.

The changing iteration figure is what gives rise to the crystallisation/organic growth appearance.

(Actually the same algorithm is applied in the first animation, but it doesn't really show. There is still an advantage, that the initial frames render very quickly, saves time, it gradually gets slower as the magnification increases.)

[Laird]

Oh, the website seems to shrink it.

Yep, Image Auto-Resizer is installed on this board so as to reduce the overall size/bandwidth of our images. Glad you found a way around it to accomplish your and David's goal.

Yes, that second one is just a very ordinary Mandelbrot rendering. One of the things which is obvious when starting to zoom in is that a lot of areas look black or empty until the (upper limit on the) number of iterations is increased. I'm sure it's not an original idea, I came upon my own idea for changing the number of iterations very gradually. Start with too high a figure and the image is filled with fine detail which actually hides rather than reveals what is there. So it starts off with a few hundred iterations per frame, ends with a few thousand.

My aim was to keep a certain amount of black there, it is like the sky against which a tree can be seen, whereas a tree in a forest is less visible.

The changing iteration figure is what gives rise to the crystallisation/organic growth appearance.

(Actually the same algorithm is applied in the first animation, but it doesn't really show. There is still an advantage, that the initial frames render very quickly, saves time, it gradually gets slower as the magnification increases.)

Zooms are very nice, but it would also be fun to carry a parameter where the effect would be non-linear. For example, the complex value C is fixed for a Julia set (if I remember rightly) so I imagine if this parameter were varied slowly all the structure would squirm and wriggle in an interesting way.

David

Zooms are very nice, but it would also be fun to carry a parameter where the effect would be non-linear. For example, the complex value C is fixed for a Julia set (if I remember rightly) so I imagine if this parameter were varied slowly all the structure would squirm and wriggle in an interesting way.

David

I'm not quite sure I understand - though to be fair my code is very old and some of it I haven't looked at in detail for decades. I'd be interested to see an example of the effect you describe. Youtube is full of Mandelbrot zoom videos - including mine. Can you point me to something which others have done to illustrate the 'squirm and wriggle' please.

That looks as if it is a binary file (as opposed to a text file), so presumably the dots represent non-printing characters, so they represent more information than if they were strings of dot characters. I suppose it rather depends on how much of that is boilerplate.

I take it you make that file with some sort of generator program.

I had your previous file up as my wallpaper, and when I loaded the new one, it was like putting on the right pair of glasses - the fractal emerged crisply from the blur.

It isn't as pure as Z = Z^2+C.

David

You can make the file direct in M3D.  Its one of the standard parameter files and somebody else with M3D can paste it into their copy to play with.  It's a common way for people to get to understand the program.  No it isn't as pure as  Z = Z^2+C although it's standard Quaternion is a 3D Mandelbrot.  When cut in half and a Julia is taken from it it can be quite beautiful.

   

Or you can turn a full Quat into a Julia

   

I'm not quite sure I understand - though to be fair my code is very old and some of it I haven't looked at in detail for decades. I'd be interested to see an example of the effect you describe. Youtube is full of Mandelbrot zoom videos - including mine. Can you point me to something which others have done to illustrate the 'squirm and wriggle' please.

Well there is a different Julia set for different values of C. It isn't zooming. So a video in which C changed in very small increments would look very impressive I think.

Well there is a different Julia set for different values of C. It isn't zooming. So a video in which C changed in very small increments would look very impressive I think.

I checked to see if TieraZon has an animation function and it does, but only for zooming and panning.  Sadly it has no way of automating seed changes.  I'll have a look at some other programs.  Maybe Chaos Pro has something.  If not, Gimp has a fractal explorer and animation tools so I might be able to set up some automation there.

Well there is a different Julia set for different values of C. It isn't zooming. So a video in which C changed in very small increments would look very impressive I think.

There is an example of this here: https://www.reddit.com/r/math/comments/b...ing_the_c/

There is an example of this here: https://www.reddit.com/r/math/comments/b...ing_the_c/

Yes, that is what I was thinking of! It might look even better if you zoomed into the Julia set and moved the value of C correspondingly more slowly.

Yes, that is what I was thinking of! It might look even better if you zoomed into the Julia set and moved the value of C correspondingly more slowly.

Yeah.  A closeup of one of those spirals morphing would be pretty awesome.