Various thoughts simultaneously came to mind for the title of this piece ranging from weird, weird and wonderful, bizarre, even creepy. The seed arose with Mister Sierpiński – and I wonder if you have heard of him? It was only by one of those weird, wonderful, bizarre convergences by which I came to make his acquaintance. You may have read the explanation of my triangle logo in the about page? A couple of years ago I came across this diagram and thought: "Well, that's pretty cool" – it's a fractal, but I didn't think much beyond that.
A few weeks ago I read a reference to the Sierpiński triangle and it piqued my interest so I followed the link. There are various methods of constructing the triangle but I like the 'chaos game' most of all as it reflects the inexplicable yet clearly mathematically repeatable amazingness of nature, of the world that we live in. Have a look at this video
For six variations on construction see also
For a more technical review of the triangle and it various constructions see also... and I liked the comment here that the triangle: "appeared as a decorative pattern many centuries before the work of Sierpiński." Nothing new under the sun.
It seems to me that evolution follows a similar, chaotic pattern with the result being this incredibly ordered, amazing, and kind of weird, chaotic world that I live in and the very body that I seem to inhabit in that world. The first video shows 30,000 iterations – and how many iterations has it taken to arrive at this particular shape of the world, the universe? And after another million, trillion iterations? Taking the triangle as origin with a given algorithm the outcome is predictable but we can only guess at our origin and ongoing, evolving algorithm. I am not writing here to prove anything or to present an argument just simply to share my awe. One aspect I can't help considering was what was it that caused me to engrave the basic double-triangle on my alms-bowl lid over 30 years ago? Of course it is totally useless to speculate but I nonetheless find it interesting to muse on the 'why'? — of so many things in life.
Another interesting fact of nature that comes to mind is regarding DNA. Each strand of DNA is about two metres long and if every piece was strung together it would go to the sun and back over 400 times. And that's all packed inside your, cosmically speaking, miniscule little body – along with all the other extensible bits and pieces. Wow!
And there is so much 'wow' still to be realised, to be experienced by each of us in our lives. The triangle exemplifies the expression "joining the dots" and the limited number of dots that we each have reveals only a small part of the full picture. You do need to be a little dotty to want to see the complete nature of reality. The majority of people are generally happy and satisfied with a workable approximation, with enough information to bring enough desires to fruition.
And this is a pretty neat mind boggler... 
Something to muse on.
PS: Wacław Sierpiński: 1882-1969. A Polish mathematician known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions, and topology. He published over 700 papers and 50 books. Three well-known fractals are named after him; the Sierpiński triangle, the Sierpiński carpet, and the Sierpiński curve. Cool dude!
PPS: I am still exploring the tone and extent of this blog and feel to some extent that this piece is a tad outside of the general direction. Is it unduly tangential, irrelevant or overly personal? Even so... it is.
PPPS: I have another 'more normal' piece underway, somewhat along similar lines to this... evolution/change... change/stillness... but quite a bit of my time has been going into building a shrine. This is now complete so I will look to complete the other text.