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Wednesday, Nov. 13, 2024

12:56am EST

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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:

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 22, 2024 at 2:16am

#1077115

Landmarks

I don't use fitness apps, so I have no idea how many steps I took yesterday, or how many kilometers they added up to. But both numbers were very, very high.

While I was still exhausted from the trip, my contact here texted me around lunchtime. We'd never met. A mutual friend introduced us. It's probably only the mutual friend that kept us from going "what if the other's a psycho killer?"

Anyway, she's like "I'll be at [landmark] and we can meet at 1 o'clock." (She's American, incidentally, so we're texting in English.) At that point, it was 12:10. I checked Maps. Walking to [landmark] would take 45 minutes. I can just make it...

...except that I'd be walking through one of the most historic and architecturally interesting parts of Paris, and there is no way I would be able to resist stopping and gawking at something. Especially when the destination was on the other side of the Seine, and what foreign tourist can NOT stop and look at the river while crossing it? Maybe someone with more self-control than I have, but certainly not me.

So we met here at the hotel and started walking. I won't bother you with all the world-famous shit I saw yesterday, but there was a lot of it and it's world-famous and it's still thrilling to see that shit in person. Just one example: my hotel is a couple of blocks from the Louvre. Well, a couple of blocks from one corner of it, maybe a kilometer from the opposite corner. It's that big. Even without going in, the building itself is a work of art. And we didn't go in anywhere; it was Saturday and the tourism was in full force, creating chaotic crowds.

Hours later, we parted, and I made my utterly exhausted way back to the hotel. Along the way, though, I paused to snap a picture of perhaps the most culturally significant of all of Paris' landmarks, located on Rue de Rivoli.

Because, though I may have gotten some of the details wrong, it was here where, sometime around 1990, famed American visitor Vincent Barbarino discovered that, in France, a Quarter Pounder with Cheese is not, in fact, called a Quarter Pounder with Cheese, but a Royale with Cheese. Because of the metric system. These events were related in the documentary, "Pulp Fiction," which depicted quite the embarrassing and tragic ending for Vincent, but at least he got to spend time in fine Parisian restaurants.

6 Like • Comment • View 2 comments

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