In the mean time, I’ve been playing around with angularjs, plus have been installingÂ laminate floors in my house, and I ran into How to fold a Julia Fractal a few weeks ago. Â What a fantastic use of 3d at the top of the page, though it doesn’t scroll well on any of my systems. Â It’s inspired me to rethink my approach for building interactive demos, and the UI of this site. Â Fun stuff ahead.
Tomorrow morning I’m doing a tough mudder. It’s going to be fun and hard, and I’m planning to have a great time.
What is that, Morse code? That my friends is the cantor set. It is one of the examples of basic topology and one of the objects that highlight many of the non-intuitive aspects of infinities.
The most common construction is to take a line and remove the middle third. Next you remove the middle thirds of the two remaining segments. You keep removing the middles of every segment that is left. If you could continue for ever, you would be left with an infinite “dust” of disconnected points.
We can build one with two simple transforms. Just contract by 2/3rds at two different points and the attractor is a cantor set. The next images are going to be simple tweaks of the cantor set, and the fractal space will grow from there.
This image has the 180 angle adjusted to roughly 60 degrees. It looks very little like the original image now.
This image has the scale for both transforms adjusted as well as the angle of the 180 rotation adjusted. You can start to see how quickly these images change into something unrecognizable as being related to the original image.
This is similar to the last one, but the angles are 180 and 90 ish. You can see the similarities with the last update.