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Friday, Nov. 15, 2024

11:52pm 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:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

January 17, 2022 at 12:03am

#1024811

Bullshirt

And another from "JAFBG"

[XGC]:

What minor inconvenience drives you fucking mad?

I think I'm one of those people who freak all out of proportion when something minor happens, but if it's major -- like when my car got totaled -- I tend to stay cool and focus on dealing with the problem.

I'm sure there have been exceptions to this, especially on the "minor problem" side. If I'm in the right mood, I can brush it off.

But there's one thing that really shouldn't bother me as much as it does, and that's clothing pricks.

No, I don't mean douchebags who wear shitty fashion. I mean, like, I put on a T-shirt and something in the seam or whatever irritates my skin. There's a tiny pokey thread, or whatever, and it digs into my skin, but when I go to look for it, I can't see anything. And then I put the shirt back on and it continues to be irritating.

This is absolutely rage-inducing, especially when I'm in a hurry and I have to dig through the clean laundry basket (don't judge; I'm a single man) to find a different shirt, hopefully one without stray pokey things.

Worse, of course, is when the problem doesn't manifest until I've thoroughly left the house. I'll be sitting there at the movie theater, munching on popcorn, enjoying the flick (or not, which is also enjoyable because I can then rehearse how I'll rag on it in a one-sentence movie review), and there it is, like a needle scratching at my skin. It's enough to turn a four-star movie into a three-star movie. "Loved the action sequences and seamless CGI, but my goddamned shirt was all scratchy."

Then I have to walk home after the movie's over with a shirt that has obviously come to hate me for making it sit through a stupid action movie.

And then when I look at the area, there's maybe some redness, but no actual pinholes.

So maybe my skin is hypersensitive, or maybe I should quit buying cheap-ass T-shirts -- still, after doing a load of laundry, that particular shirt doesn't bug me anymore, but another one, one I have never had problems with, starts doing the pokey thing.

Speaking of movies, I was really hoping to go see Licorice Pizza, but apparently it's out of the local theater now. Not a lot of point in finding it on streaming; the whole reason I go is to experience the movie on a big screen, with other people, and to drink beer. I meant to go last week, but a bunch of stuff kept getting in the way.

Hopefully the snow we got -- which wasn't even anywhere close to the predicted foot -- will melt enough that I can walk over there sometime this week to see... I don't know. Something. I'll just have to give myself enough time to change shirts before I go, just in case.

8 Like • Comment • View 1 comment

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