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Wednesday, Nov. 13, 2024

1:04am 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 11, 2024 at 11:48am

#1076615

Drop and Gimme Twenty

Somewhat predictably, I'll take a break from the usual today in order to blab about this being my 20-year anniversary here.

Unfortunately, I said most of what I wanted to say back on September 1, as we began the site's 24th anniversary: "Four and Twenty"

Having my own milestone so soon after that of the website itself, though, is kind of like I'd imagine it would feel like for your birthday to be on December 26: everyone's burned out on celebrating, including me. Especially me.

Which is fine. I'm on board with celebrating actual birthdays, but membership anniversaries are just, well, whatever. Still, this being the 20th, one of those nice rounded-end numbers, I felt I should say something about it.

Things were a bit different back in 2004. Smartphones weren't ubiquitous yet. The internet hadn't become a mire of scams, ads, and influenzas. And a certain other event that took place on a September 11 was still fresh on everyone's mind.

I hadn't intended to join on the 11th, for that reason. I tried to create an account here the previous day (my dad's birthday, and he was still alive back then, so already a significant day for me), but for whatever technical reason, it never took. That's also how my username got the annoying 02 at the end; while the account didn't work, my attempt was enough to block off just "cathartes" as already in use. It's been long enough that I don't remember all the details exactly (hell, 20 days is probably long enough for that, for me), but I vaguely recall creating this account with help from a friend who was already a member, shortly after midnight, forcing my account anniversary to be on a day that was already infamous.

I've considered changing my username to something else, but never went through with it. It's kind of part of my identity now, so I'm ambivalent about the idea.

So, I'll just finish by posting what I'm pretty sure was my first item on here, created on September 11, 2004—but which I'd written some years earlier: "Ghost Poem #1"

[ASR]

Odd that it was a poem, I suppose, because I'm more of a fiction writer and, now, a blogger, but I suppose it was something quick and simple to put up here to get started. And even back then, when I had an actual job and a spouse, I was all about quick and simple.

Some things don't change all that much.

6 Like • Comment • View 4 comments

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