I'm getting error 403 ("no permission to access") for your images.

I can see the images now. It seems to me that they are not fully analogous to the original Sierpinsky triangle. The 3 triangles are scaled such that they just about touch each other. But your images with squares, pentagons, hexagons ... have slightly smaller polygons.

And there is one more degree of freedom that you could explore (this is not a request, just a suggestion): the individual polygons could be rotated. This influences where and how they can touch each other, so consequently this also influences the size factor by which the polygons are scaled down in each iteration.

I am doing the polygons like this:

1 - Go to one random corner.
2 - Move some constant part of the distanse to one random corner and set a point there.
3 - Repeat from 2.

What I am trying to found out is the constant part to move to next random point.

n-gon	part
3	2
4	?
5	Golden Ratio  (1.168...)
6	1.5
7	?
8	square root of 2
9	?
.	?
.	?
.	?
Infinity	1 (I think)