Here be dragons…

Hello, will release a new beta in the next days – mainly technical updates and bug fixes, but this will be the last purely technical update. So next stop will be some new features. But in the meantime, here is the new Fractview icon:

Yes, its from Seahorse valley. But it was taken in a different way. Let me explain: The mandelbrot set serves as a map for julia sets in it. What is not known that much is that you can invert the mandelbrot set by using the reciprocal of the coordinates, kind of turning the mandelbrot set inside out.

Inverse Mandel.png

Mandelbrot set of the formula “mandelbrot(z, 1 / p)”

The heart-shaped body effectively becomes a drop.

The other day, I was browsing through sea horse valley on my smartphone when suddenly I had an idea: In this ‘drop’ fractal, features close to the origin (0, 0) are enlarged to infinity while features far away are centered. What about not using the origin but some other point that exhibits more interesting features than the (boring) origin?

So, the formula that I was exploring was “mandelbrot(z, 1 / p + somepoint)”, and the results were so amazing, I immediately created a new icon for Fractview (the feature graphic of this blog post).

Let’s look at the result: First, the second biggest feature in the mandelbrot set is  the circle that is centered at -1:0. By inverting it using -1 we obtain a rounded inside-out mandelbrot set. It reminds me of a fractal solar eclipse.

Mandelbrot Eclipse.png

Mandelbrot set of the formula “mandelbrot(z, 1 / p – 1)”

Now, that  is a nice plate. But where are the dragons? Well, I tweaked the Default fractal program a bit (you will find it in the presets at the end of the article) and now apart from the “julia set” flag, there is now a “reciprocal” flag that uses the current julia point as parameter. If that was a bit complicated, just import these favorites from my public Google Drive in Fractview. You will find “Default with reciprocal” there. Just browse to a nice spot, eg in the sea horse valley, select “Center” for “julia point” in parameters and toggle the “reciprocal” flag. Looks boring? Remember – features that were close before are now far away, so zoom out, and then

Enter the dragon.png

Enter the dragon

You will find the dragon at the edge of the known world. On your way there, you will find weird shapes (well, these are fractals, right?). Really weird I mean.  I found this when looking at a julia island in the dentrites:

Seahorse lightning.png And after zooming out for another factor of 20 it completely changed: Confused Dragon.png

Yes, both of these images are just a zoom factor of 20 away (the above image is located in the center, you can see it as a small dot right in the center of the lower image).

All of these lovely images are part of the collection linked here again. 

Finally, a lovely image using 0.279 as julia point:

Dragon (0.27x0).png

That was some fun on the weekend 🙂

Stay tuned for an updated beta version in the next days btw, and until then enjoy the endless possibilities of Fractview. Btw, 5600 users and counting.

Cheers, and enjoy your weekend

Karl

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This entry was posted in Fractals, Mandelbrot, Updates. Bookmark the permalink.

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