Hat Tip to @emilyhasbooks on Twitter.
This was pointed out to me last night, and I chilled my evil fractalicious heart with thoughts of Benoit Mandelbrot spinning in his grave in agony:
It’s a blog page [Here] on a New Agey site called Human Angels, with some nice fractals, but very little in the way of valid factual substance, allegedly using religious lore from Hindu, Mayan, Hopi and Jewish scripture, the long-since debunked Bible Code, the Mayan calendar 2012 nonsense, with a a bit of the appeal to quantum physics fallacy and the silly invocation of the geological record to make claims of predicting the future, presumably in ways impossible for mainstream science.
The first sentence of the page I have no issues with:
A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity.
Okay, there’s nothing off about that, but after that, the text goes down the proverbial rabbit-hole and into the land of meaningless word-salad immediately following:
All of the manifested universe can be described as fractions of dimensions, or fractalic, while the whole dimensions themselves are of infinite measure. From the whole dimensions are derived the finite dimensional parameters which define what we know of as space/time.
I’m tempted to say WTF??, though I’m aware that the universe is NOT fractal, but is largely relativistic on the macro-level and quantum on the micro-level (Individual bosons, like photons, are discrete packets of energy as shown by experiment, not infinitely divisible into self-similar parts.) as far as anyone can show at present.
Never mind that New Age claims, like those of Old Time religion, lean heavily into bald assertions of knowledge that is not and cannot possibly be actually known given the fact that wishful thinking to the contrary, believers don’t really have any special powers the rest of us don’t.
This one really did it for me…
Part of the make-up for a fractal, is the idea of a pattern repeating within a pattern. This is how Gregg Braden explains the cyclic patterns of time experienced on the earth. Basing it on two major cycles; the 5,125 year cycle that it takes the earth to once again cross the galactic equator of the Milky Way, and the 25,625 year cycle that represents the progression of the equinoxes, Braden paints a picture of the possible changes life on this planet faces.
Sorry, nice metaphor, but it means nothing. The claim of passing through the galactic “equator” every 5,125 years is based on a false premise, two actually: The Earth will not be passing through the plane of the galaxy’s disk in 2012, though as far as the sun is concerned, it does cross the equator twice each year, and there’s nothing at all special about it, and no evidence that space-time is fractal – See Planck length and Planck time for the reasons why…
…These are not the droids you’re looking for…
Second, and finally, this idea that ancient civilizations knew more than we is literally old and illogical, an appeal to antiquity fallacy:
The Mayans didn’t have nearly the knowledge we do of the age, nature, and shape of the galaxy, and even we don’t know it precisely, so any claim that their calendar took into account Earth’s passage through the mid-plane of the galaxy’s rotation is simply silly. No credible archaeologist would make such an assumption of facts not in evidence. We know now far more than they, and their ancient writings and monuments have value as historical records and artifacts only.
As tempting as it is to cut loose with the snark, I’ll have to refrain from indulging myself this time to file this one away in my collection of amusing and possibly unsinkable misunderstandings of reality.
- Fractal Friday it is… (buddhakat.wordpress.com)
- Fractal Friday… (buddhakat.wordpress.com)
- The Fractal Dimension of ZIP Codes (wired.com)
- Inside The Incredible World Of Fractals, The Beautiful Patterns That Investors Use To Understand Charts (businessinsider.com)
Posting essays has been a little slow last week, and a lot of you I’m fairly sure have noticed the fractal artwork featured on this site over the last few months, especially the weekly feature image posted each Saturday.
Let me assure you that all such featured images, as well as the background and header for the Call are my own work, creating itself through me by way of an amazing shareware app called Fractal Domains, to which I am greatly in debt for its usefulness.
Most of my non-blogging time, when not studying, has been well-spent the past week creating and updating customizable templates for the software that I use to more efficiently and effectively produce the images I use.
First, let’s get something out of the way: The following thumbnails are images NOT of my creation, but are public domain work that I obtained from Wikimedia Commons before creating my own earlier this year:
There. That should be all of them…Breathtaking as some of these no doubt are, they are not mine to claim credit for, just to clear up any misunderstandings that may arise from my use of them.
See Wikimedia Commons for Fractals for the proper attribution of these images.
I’m hardly an expert on maths, but I just love fooling around with numbers, and this is a big plus in generating my own templates, most of which are identical for each of the Mandelbrot, Halley and Newton sets, and their derived Julia sets, save for the numerators, and with a few, other portions of the numerical formulas used by the app to tell the computer (I have a Mac, as many of you know…) how to produce the graphic images that result.
The basic form of the numerator is this: z³-1 — Pretty simple, but I like a little more from the app than just a stock setting, so here’s an example of one of the custom-programmed numerators saved for a template:
This change to the basic formula in a set using Newton’s method (Yes, I’m referring to the cranky but brilliant English guy who co-invented calculus and was allegedly beaned by an apple good according to the group R.E.M…) results in an image looking sort of like this, depending on how far I zoom into the image, where I zoom into said image, and what color-scheme I choose:
One thing I’ve discovered is that breaking the exponents in the formulas into manageable bits keeps the program from quitting as it would if I had just added all of the exponents together into a single term, and I’ve found out that it produces a different image as well, such as with the numerator of z¹⁰+z⁵-1 as opposed to combining them as in z¹⁵-1, as with the following for each in turn, again using Newton’s method:
Note the differences. Fractal domains is for the moment the biggest and most favoritest time-waster on my desktop, and so worth it.
I think, though, that it’s a Mac-only app, and I’m not sure if there are any plans for a Microsoft-compatible version.
The unregistered shareware comes with basic features, that can be used without restriction, and without an expiration date for the app that I’m aware of, but I paid only $20 online for the registration code that lets me use the full features.
If you’re as into algorithmic art as I am, and have a Mac or similarly compatible system, check this app out, and start making your own truly incredible images.
For me, making fractals this way is an exploration of what’s possible each time I produce a batch of images, while saying to myself, “What happens if I click on this, or fiddle with this number?”