Fractal Maze

[Spycraft]

I am intrigued by a concept I call the "Fractal Maze".

I had this concept when watching one of those beautiful fractal zooms into a 3D fractal. The concept seems fun enough, but leads to some Mathematical ideas.

Basically, OK, I've zoomed into this fractal, but having forgotten the path I took, how do I get out of here?

Well since Fractals are generated by an algorithm (essentially), the path out of the Fractal must always be mathematically quantifiable. Thus no matter where you are in the fractal you must be able to in some way describe, mathematically, where you are exactly in the fractal and thus work your way backwards to outside the fractal (where most fractal zooms begin).

That being said, I don't know what those formulas would be! Or how to generically describe your position in all fractals and thus describe the path back out!

But the logic is sound, it should be possible, and I would love to someday see the Math that describes how to navigate a "Fractal Maze".

 

[RWNJ]

I am intrigued by a concept I call the "Fractal Maze".

I had this concept when watching one of those beautiful fractal zooms into a 3D fractal. The concept seems fun enough, but leads to some Mathematical ideas.

Basically, OK, I've zoomed into this fractal, but having forgotten the path I took, how do I get out of here?

Well since Fractals are generated by an algorithm (essentially), the path out of the Fractal must always be mathematically quantifiable. Thus no matter where you are in the fractal you must be able to in some way describe, mathematically, where you are exactly in the fractal and thus work your way backwards to outside the fractal (where most fractal zooms begin).

That being said, I don't know what those formulas would be! Or how to generically describe your position in all fractals and thus describe the path back out!

But the logic is sound, it should be possible, and I would love to someday see the Math that describes how to navigate a "Fractal Maze".

I didn't know they had 3D fractals. Interesting.

 

[RWNJ]

I am intrigued by a concept I call the "Fractal Maze".

I had this concept when watching one of those beautiful fractal zooms into a 3D fractal. The concept seems fun enough, but leads to some Mathematical ideas.

Basically, OK, I've zoomed into this fractal, but having forgotten the path I took, how do I get out of here?

Well since Fractals are generated by an algorithm (essentially), the path out of the Fractal must always be mathematically quantifiable. Thus no matter where you are in the fractal you must be able to in some way describe, mathematically, where you are exactly in the fractal and thus work your way backwards to outside the fractal (where most fractal zooms begin).

That being said, I don't know what those formulas would be! Or how to generically describe your position in all fractals and thus describe the path back out!

But the logic is sound, it should be possible, and I would love to someday see the Math that describes how to navigate a "Fractal Maze".

I didn't know they had 3D fractals. Interesting.

If anyone is interested, you can download the software used to create this here...

Mandelbulber