Fractal Explorations

[TheBigDog]

This thread is dedicated to the discovery of beauty and wonder within Fractal sets. Attached is a link to another thread where we discussed fractals, and a three tools for exploring fractals are posted.

I wrote the Fractalator 2.0 to make it super easy to look at fractals any way you want. One of the things that got under my skin a little as I wrote it was the fact that due to the limited precision of numbers you eventuall start getting distortion in the Fractal views. But when I sat today and did the math I became far less irritated with the limitation. If you load and run the Fractalator 2.0, it has a warning when you get to about 10.5 billion times zoom that you may start seeing distortion. You can continue zooming to over a trillion times zoom, with distortion kicking in some time after the warning. But here is the reality of that statement. On a 96 dpi screen, the default fractal picture is 5 1/3 inches across. Zoomed to the warning that original picture is now the equivilant of 883838 miles across. The whole picture at that point is 781,170,288,746 square miles. That is almost 4000 times the area of the whole earth. So even if just 1% of that area yeilds interesting pictures, imagine all that there is to see. And when you zoom past the distortion warning you can be looking at details of a surface area equal to the area surrounded by the orbit of the moon.

Imagine the possibilities.

Fractal Geometry of Nature

If you want to use the Fractalator you can find it at the above link. It runs on windows using .net framework (native to XP). You can post your favorite list of Fractals here so others can load and view them on their own copy of the Fractalator, or you can save them as bitmap, jpeg or gif and post the pictures. If you have another favorite explorer you can let us know about it too.

I will post some sample lists and color pallets later.

Bill

Pyrotex's Mandelbrot Explorer can be found here. It is a java program.
Fractal Geometry of Nature

[Pyrotex]

Thank you Big Dog! Looking forward to some wild zoomie pix!

[TheBigDog]

Math error! I was off by a bit when calculating the zoom. The warning is not at 10.5 billion, it is at 10.5 Trillion! That means that when the warning comes on the initial picture would be 883,838,383 miles across. Or a total area 28.7 x greater than the area encircled by the earth orbiting the sun! That is a huge frigging picture!

Here are some Fractalator toys... Color Files! I have been making different ones to play with. The coolest by far, in my opinion is Black Light. Just detach and unzip. Then under the SAVE function you can load a new color file. It will not disappoint!

Bill

[TheBigDog]

And here are some sample Fractals. You can load them by unzipping them and then using the change list function.

I have just really begun to play around with this. There are some neat ones in here. Look at them using various color schemes so see new details. I really like the Black Light scheme. Coooool!

Bill

[TheBigDog]

I have made some fixes to the Fractalator. It had some issues with the color control, and the loading and unloading of color files. Those have been fixed. The attached file has everything you need to begin using and enjoying the Fractalator.

Don't let the small size of this file fool you. Enjoy!

Bill

[Vicarious]

Here's an interesting thought about the Mandelbrot set. Just how far in does that pore on the right side go? It gives the impression of continuing infinitely, getting smaller forever as I pan left. Any fractal program I have tried will only go so far before I have to increase to a million or more iterations. It's too slow like this, and I get the same results.

An easy way to figure this out is to test points inside the cardioid that are very small on the y axis (C axis?), so that they are very close to the x axis (Z axis?). I'm shaky on how exactly to do this.

[TheBigDog]

Originally Posted by Vicarious

Here's an interesting thought about the Mandelbrot set. Just how far in does that pore on the right side go? It gives the impression of continuing infinitely, getting smaller forever as I pan left. Any fractal program I have tried will only go so far before I have to increase to a million or more iterations. It's too slow like this, and I get the same results.

An easy way to figure this out is to test points inside the cardioid that are very small on the y axis (C axis?), so that they are very close to the x axis (Z axis?). I'm shaky on how exactly to do this.

It appears to go into infinity, but it is actually approaching a point that it can never reach. Remember the dimensions that you are looking at when in extreme zoom. I went well over 1 quadrillion zoom on that point When zoomed that far in the whole picture covers a bigger area than the soalr system. And all you are doing is moving a few feet to the left and finding another round point. So you zoom in again and turn up the iterations and move to the left a few more feet. Now the whole picture is 10 times the size of the solar system and you move a few feet to the left again. Each time you zoom in the distance you actually move onn the picture is reduced. The spot I like is the point where the spire on the left meets the circle around the whole structure. Mathmatically these different geographic points seem to be proportions of the whole, which may give you the anwser to your question.

Bill

[Vicarious]

In your opinion, the dimple that forms the top of the heart approaches a specific x-value, existing only to the right of that value. At a very small distance to the right of this x-value, the dimple can be found, but it will also be very small.

Yes?

[TheBigDog]

Yes. The dimple on the right appears to approach, but never reach the horizontal coordinate of 0.25. If you look at the map mutton you can see the centerpoint of your current view. I cannot get that spire to cross that coordinate on my screen.

Bill

[Vicarious]

So how are iterations increased in fractalator? I can see the number, but not change it.