4 ms·
One way to think of it is that for example bighorn sheep: they have horns formed in a physical spiral shape, whereas a galaxy may look like a spiral, but is com
by warent 5y ago
One way to think of it is that for example bighorn sheep: they have horns formed in a physical spiral shape, whereas a galaxy may look like a spiral, but is composed of myriads of individual stars, organized in that shape.
The horn is composed of myriads of individual particles organized in that shape. The illusion is stronger but it's no more physical than a galaxy. Then the fractal which is composed of myriads of points is the same.
I don't get what the author is saying, but I think they're just adding confusing noise to their message by mixing some incomplete philosophy around the nature of objects.
- scotty79 5y agoI think he's saying "Wow, those fractals! How profound!" For me the amazing thing about fractals is that they come often as a result of very simple equations. They show that simplicity and complexity go hand in hand.
- pmoriarty 5y agoYou can get complexity from a simple pseudo-random number generator. Fractals are more interesting than PRNG's to me because they not only result in complexity from simplicity, but because of their self-similarity and beauty.
- scotty79 5y agoPseudo-random generators also have this self-similarity and beauty if you dig into them deep enough. And if you take an arbitrary thin slice through a fractal it looks pseudo-random. Consider equation like x <- kx(1-x) that turns chaotic for some values of k. When you plot its behavior for various values of k around that point you'll see weird self-similarities like in fractals on the border of apparent chaos.
- Sharlin 5y agoTo be fair, there is sort of a qualitative difference between the two: the spirals of spiral galaxies are density waves moving independently from the orbiting stars themselves. When it comes to fractals, there is a much deeper and fundamendal distinction that can be made, though: the difference between connected and disconnected sets. The Mandelbrot set is connected (and indeed simply connected), no matter how much some of its regions might look like made of disjoint components. There can always be found "tendrils" connecting everything to the main bulb. On the other hand, Julia sets are either connected (precisely those that correspond to points in the Mandelbrot set) or disconnected (in which case they are "dust" made of uncountably infinite disjoint points).