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Sunday, Jun. 30, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Montana

about 13 hours ago
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

about 13 hours ago
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

about 16 hours ago
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

a day ago
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

1 Like

June 27, 2024 at 9:37am

#1073235

Wave Rider

Art History. Another subject I know almost nothing about (though, no, I'm not here to mock liberal arts degrees). Lack of knowledge has never stopped me from blogging about something, however. So, from The Conversation way back in 2017:

Friday essay: from the Great Wave to Starry Night, how a blue pigment changed the world

If you're wondering why I picked this article in the first place, well, there are several reasons, not least of which is that it's tangentially relevant to the title of my blog.

How? Well, there's a detail from Great Wave there at the article link. Now, look at this detail from the fractal Mandelbrot Set,

an iconic image of the strange and wonderful properties of complex numbers.

This is either coincidence, or Hokusai was tapping in to the same chaotic properties of nature to create that painting.

I'll save the other big reason for the end.

Hokusai’s The great wave off Kanagawa remains the enduring image of Japanese art.

And it even includes Fuji-san, which as I understand it is at least as important to Japanese art as tentacles are.

Although diminutive in scale, the importance of Hokusai’s “Great Wave” cannot be overstated. The work profoundly motivated the French Impressionist movement, which in-turn shaped the course of European Modernism, the artistic and philosophical movement that would define the early 20th century.

I'm going to have to take the author's word for that, because, like I said, I don't know much about art history.

But I do detect a whiff of Euro-centrism there. I could be wrong about that, though.

The most immediate and attractive aspect of Hokusai’s wave is its colour.

I mean, maybe? Again, I'm more interested in the fractal boundaries, its depiction of the froth on the waves. But there's good reason I'm not an art person.

The story of this blue pigment highlights the role of cultural exchange at the heart of creative discovery and ranks among the more contradictory tales in the history of art. The vibrant hue, long considered to be quintessentially Japanese, was actually a European innovation.

Okay, that's more than a whiff of Euro-centrism.

I'm not saying it's wrong, mind you. But lots of Japanese things are quintessentially Japanese not because they necessarily invented it, but because they elevated it. Tea, for example. Automobiles. Whiskey. Tempura. Anime.

In truth, it had been invented half a world away, 130 years before Hokusai’s wave broke, in an accident involving one of Europe’s most colourful figures: Johann Conrad Dippel. Born in the actual “Castle Frankenstein” in Germany in 1673, the enigmatic theologian and passionate dissector believed the souls of the living could be funnelled from one corpse to another, thus becoming the rumoured inspiration for Mary Shelley’s masterpiece, Frankenstein.

"most colourful figures?" Oh ho! I see what you did there!

In his thirties, Dippel had become captivated by the proto-science of alchemy, but like so many in the profession, had failed to convert base metals into gold.

If the spelling of "colour" hadn't tipped me off already, this sentence would peg the author as very British. Because that's a fine example of the British art of understatement. No alchemist was able to convert base metals into gold; any that said they did were perpetrating hoaxes.

He instead settled on the apparently easier task of inventing an elixir of immortality. The consequence was Dippel’s oil, a compound so toxic that two centuries later it would be deployed as a chemical weapon in World War II.

Also a quintessentially British sense of irony.

Well, the author is actually, apparently, Australian. But they're even better at irony and understatement.

Anyway, the article goes into the history of blue. Well, kind of. It may seem odd to us today, when we can go to Blowe's and get house paint in any one of millions of shades, but back in the old days, certain colors were precious, rare, or even unattainable. There's a reason purple was associated with royalty in the West.

Then:

Perhaps the single most vividly identifiable influence upon the European modernist founders is Van Gogh’s celebrated Starry Night, which owes everything to Hokusai’s blue wave from its colour to the shape of its sky. In letters to his brother, Van Gogh professed the Japanese master had left a deep emotional impact on him.

As regular readers might know, I'm fascinated by cultural exchanges like this. I don't have to know anything about art history to follow what the article is saying.

In reality, Hokusai had skillfully blended European colour and structure with Japanese motifs and techniques into a seamless work of international appeal.

One of my most prized possessions is a T-shirt that a friend gave me. It features a copy of the Great Wave. But towering over the Wave, the doomed boat, and Fuji-san is one of the other great contributions of Japan to world art and culture:

Godzilla.

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