Yehliu Honeycomb Rock loacted in Yehliu Geopark . Honeycomb weathering, sometimes known as fretting, stone lattice, stone lace, miniature tafoni, and cavernous weathering, is a form of weathering common to arid or coastal granites, sandstones, and limestones.
Are fractals simple or complicated objects? Or perhaps both? The beauty and attraction of many fractals stems from their complex and intricate form, with ever more detail becoming apparent under increasing magnification. Yet many fractals depend on a very simple rule, applied over and over again, a process called iteration.
The Mandelbrot set is perhaps the best known example. It is completely determined by the very simple formula z2 + c, where z and c code points in the plane or on a computer screen in terms of ‘complex numbers’. If, starting at 0 and repeatedly applying the formula to move from one point to the next, the sequence of points stay ‘close to home’, then c belongs to the Mandelbrot set and is coloured black in the pictures. If, on the other hand, the itinerary rapidly shoots off or ‘escapes’ into the distance, then c lies outside the Mandelbrot set and is coloured according to the rate of escape.
This simple rule is very easily programmed on a computer. Yet the Mandelbrot set is an extraordinarily complex object. It has a prominent cardioid, or heart shape, surrounded by near circular buds, which in turn have smaller buds attached to them. On closer inspection, stars, spirals and sea horses become apparent. Joined to these are many fine hairs on which lie miniature copies of the Mandelbrot set itself, and increased magnification reveals an endless gallery of ever more exotic features.
For its appearance alone, the Mandelbrot set would merely be a fascinating curiosity. But in recent years its remarkable mathematical properties have become enormously significant. Naturally associated with each point c of the Mandelbrot set is another fractal, called a Julia set. If c is in the main cardioid, then the Julia set is a closed loop, if c is in the largest bud, then it is formed by infinitely many loops, meeting systematically in pairs, and so on. Moreover, the Mandelbrot set is ‘universal’ in that it codes the behaviour of iteration by many formulae other than just z2 + c.
Images courtesy of Kenneth Falconer.
have a look at these awesome illustrations from by buddy SHVLFCE!
anybody read this?
i didn’t pick it to read right nownah i totes had a change mind so yeah i am reading it, but some input would be kind of nice because, well, it seems a tad odd
the way it’s set up
it was mentioned quite a few times in my internet perusing, and a lot of people were talking about how long/hard (i’ve been reading for 7 months…) of a read it is so of course i had to buy it
and i mean, it’s a big book, gotta be at least 500 pages (i didn’t check) but
let me show you
any input you can give me on what i’m getting myself into here would be cool
This is the best book i have ever read, it took months to read it and i couldnt even finish it the second time round, i seriously recomend it though
This book is the bomb. It is awesome. It is terrifying. I haven’t yet had the leisure to just read the bloody thing start to finish, but it’s one of those books that you’re reading all haha this isn’t scary and then you look up and the walls are closing in around you and your hallway may or may not be there it might be stretching it might be shrinking it might be nice to close that door now. I went to the 7-11 to get a snack in the middle of reading this book. All the shelves had been rearranged. Nothing was where I left it. It scared the shit out of me, I had to take some very deep breaths here. And you would know why if you read this book, which could be catalogued as ‘architectural horror’.
I’m totally going to buy this book. D:
This book is beyond fantastic, I recommend it to anyone who enjoys reading and just books in general as a medium. The content itself is amazing and it made me think about exploiting your medium as an artist.