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Sunday, Nov. 10, 2024

1:39pm 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:

Kåre เลียม Enga

a day ago
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

a day ago
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

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

July 23, 2024 at 9:14am

#1074310

Holy of Holies

This month's penultimate entry for "Journalistic Intentions"

[18+] takes us to the Great White North.

Montreal

A while back, a friend of mine was getting ready to visit NYC for the first time. (I promise this is relevant to the prompt.) She knows I go there fairly regularly, but every time I wanted to give her advice or suggestions, I managed to restrain myself. "I'll answer questions if she asks," I thought to myself. "It's more fun to discover things for yourself there."

And then, one day, she texted me with, "Where's the best place to get bagels?"

I immediately responded with "Montréal."

"Asshole."

There are, of course, plenty of great bagel places in New York. While I can't personally vouch for the "Montréal" answer, having never been there, I've heard it from so many different sources that I have accepted this superlative as Truth.

Which led me to wonder: How did this Francophone city in the upper reaches of North America become the Holy of Holies? (Get it, because bagels have holes? I'll be here all week.)

Obviously, it has to do with the Jewish community there. But the origins of this particular toroidal carbohydrate module stretch back, not to France, but to Poland. Like every near-perfect food, such as curry or pizza, though, they proved too popular to be limited to one country, instead spreading in their glorious roundness all over the globe.

It's true, however, that bagels entered the North American diet by way of New York, not Montréal. But they spread like cream cheese on a... well, they spread. Hell, there's even a great and popular bagel place right here in my very Southern hometown.

It's even one of the few foods that California does right. They can't make a decent pizza or pastrami sandwich, but there are at least good bagels scattered around California like poppy seeds on a... well, they're scattered.

As a side note, I once had a pastrami pizza. I was, of course, initially skeptical, but that particular abomination turned out to be quite delicious. Where was it? South freakin' Dakota, and I never would have discovered it had I not been stranded there for two days.

But I digress. We were talking about... what were we talking about? Montréal. I thought about going there before France, mostly to try the bagels. But I was concerned that I'd miss summer. There's a three-day window when the climate there would actually be comfortable for me; the problem is, one never knows exactly when those three days fall on the calendar. Usually in July, but not always.

Bagels, however, are a multi-season food. You know, many seasons. Like on an everything bagel.

4 Like • Comment

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