# Name of this fractal

I am writing my final paper in the field ob computer enginering my work are on fractals. Some time ago, I found this fractal. Now I need to refer to it in my work but i have no clue what is it called. I searched the internet but found nothing really useful. The only mention fractal that I found is called an outward circle but its not exactly the same. http://pixgood.com/fractal-circle.html! My fractal :

• WHat's not exactly the same about it? They look nearly identical, except you've drawn yours with solid circles instead of hollow ones. – Dan Uznanski Sep 16 '14 at 12:53
• True i forgot that the circles cross each other. It the name ok thou ? – Shawn Sep 16 '14 at 12:55
• Google Image search found this: grafika.me/node/206 – lhf Sep 16 '14 at 13:03

## 2 Answers

It looks to me like you've got a slight variation of a standard visualization of the Cayley graph of the free group on two generators. If you take a look at the Wikipedia page on Cayley graphs, one of the first images you see is something like so:

Now, if we just place disks at the vertices scaled appropriately, we pretty much generate your image:

Of course, it's fractal properties will depend on the choice of scaling factor between steps. It think I've chosen a somewhat smaller scaling factor than you to generate my image.

Fractal Kvaziklever according to http://grafika.me/node/206

• That's pseudo-clover in Russian, right? So the name is definitely wrong $-$ the fractal in the picture is missing the bottom quadrant (because it's a clover-leaf). – TonyK Sep 16 '14 at 13:48
• Close but not quiet the same. – Shawn Sep 16 '14 at 14:15