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Wednesday, Nov. 13, 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

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

Show Recent Comments

10 Most Recent Blog Comments:

Brandiwyn🎶

about 14 hours ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 23, 2024 at 4:10am

#1077168

Bière Snob

Yesterday morning got off to an auspicious start as the really quite obnoxiously loud building alarm went off.

Naturally, being American, I sat down to write an official letter of complaint to management, and prepared to give the hotel 1 star reviews on Yelp, Google, and Tripadvisor. How DARE they inconvenience a US citizen?

...yes, I'm kidding. Duh. I took long enough to put pants on, which may not have been the wisest course of action for myself, but you know me, always thinking of others' comfort. And then I proceeded down five flights of narrow, steep, half-spiral stairs that are probably older than my entire country.

I'd been awake, though not for long, when the alarm went off (hence the pantsless state, as I was only beginning to get ready to go to the hotel breakfast), so at least I didn't have another heart attack from waking up to that. But on my way down, I got to wondering whether my travel insurance would cover the loss of all my shit from the hotel burning down. Probably not, I reasoned, because insurance only covers whatever doesn't happen to you.

On the descent, I was joined by other people who also had the good sense not to use the elevator during a fire alarm (one of whom had stopped to pack his bag), and we all spilled out into the lobby, where a receptionist explained to us, in perfectly good English, that someone had made smoke in the breakfast kitchen and it wasn't actually a fire threat.

My fellow travelers grumbled and started marching back up the stairs (the elevator is one of those tiny European ones with the manual outer doors, obviously retrofitted at some point after electricity was invented), but I followed my original plan and slipped down to breakfast, where I specifically asked for le petit déjeuner bien cuit, or breakfast well done (in the sense of a well-done steak). Because I am, after all, an asshole, but at least I'm a funny asshole.

The travel agent's plans for me yesterday were: Eiffel Tower, Arc de Triomphe, Champs "Ulysses" [sic], and the Seine. But none of them involved tourist reservations; those were just their suggestions for famous shit to do while in Paris.

So, instead, I did what I always do in a new-to-me city: I found breweries.

You don't think of beer when you think of France, and generally for good reason. There are a few decent large-scale breweries in the east, adjacent to Belgium and Germany so that those countries' skill in brewing manages to spill over the border. But for the most part, French beer is, historically, liquid ass.

But, like the Anglophone countries I'm used to, France has developed a craft beer scene. I only had time to visit three of them, but my overall impression is: just like the aforementioned Anglophone countries, some of the beer is excellent, and some is... well... less than excellent.

I'd never know that, though, if I didn't try. I'm pretty sure I've said this before in here, but I enjoy tasting all beer, even the bad stuff, because, as the great philosopher said: "If everything was cool, and nothing sucked, how would we know what was cool?" (I can't remember if that was Beavis or Butt-Head.)

Now, when I say "tasting," I don't mean I got pints (or, you know, 500ml, close enough) of each one, but did the small-serving flight thing. So no, I wasn't utterly wasted when I was done. But I had achieved beerenity, which has been elusive to me lately. I might have actually smiled as I walked back to the hotel, across the Seine, and through the courtyard of the Louvre, where I paused to snap what is surely the most French photograph I could possibly shoot.

7 Like • Comment • View 1 comment

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