Kaleidoscope - a visual treat

I am trying to generate views like these:....

These images do look beautiful don't they?

I am poring over books on symmetry by Marcus Du Sautoy(Finding Moonshine) etc. 

Students of high schools such as you may create a great project out of printing these kind of patterns using your father's newly acquired laser printer.

And this one is beautiful too....

Finally last but not the least some pattern of tiles from the alhambra, Granada, Andalusia, Spain...
This one is a triangular pattern of tiles...

Can't make out this one and it is taken from some university's mathematics site... They must have found something truly amazing in these patterns.

So you must be wondering when is my project output coming... Hold your breath... I have not started work yet.

Effort put into this project would be considerable I guess. I propose to use symmetry and generate patterns by randomly generating one pattern of polygons in a part of the image and reflecting/tiling it to other parts. It looks daunting but doable. If i generate a polygon in one region and reflect it in other parts using symmetry the problem is how will I fill it. The vertices may not be in order and the polygon may be self intersecting. Will keep everyone updated in this page.