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Sunday, Nov. 24, 2024

5:16pm 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:

Turkey DrumStik

about 4 hours ago
In response to "Revisited: "Plus Ça Change...""

Hm. One thing that might be different. I might not be so completely, utterly done with approximately half of the population of the US.

Even if that had been the case, I'd be completely and utterly done now.

I might still have some tiny thread of hope for the future.

Let's see... nope. All gone.

By coincidence, my latest journal entry ends up critiquing these points (and pretty heavily, to boot).

2 Like

tj-turkey-jobble-jobble-hard-J

about 22 hours ago
In response to "Pursuit"

My grandmother used to say, "Pursuing happiness is like a dog chasing it's own tail."

3 Like

🌕 HuntersMoon

a day ago
In response to "Pursuit"

Happiness is reading your ramblings daily. True happiness is posting a snarky response.

3 Like

Robert Waltz

Nov 20, 2024 at 2:54pm
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

Nov 20, 2024 at 2:32pm
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

Nov 20, 2024 at 1:20pm
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

Nov 19, 2024 at 7:43pm
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

Nov 19, 2024 at 4:04pm
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

October 22, 2024 at 10:16am

#1078731

Stark and Dormy

And now, one of my rare posts about actual writing...

2024 Bulwer-Lytton Fiction Contest

It is a truth universally acknowledged that of all the bad opening lines of literature, with the possible exception of the one that begins, "It is a truth universally acknowledged," the one that begins, "It was a dark and stormy night" is the nadir of all possible opening lines. This was from Bulwer-Lytton's novel Paul Clifford, about which literally no one outside of academia knows anything apart from the opening line.

Like all truths universally acknowledged, it's not necessarily true. But it still provides the impetus for writers to try to do worse, generally to hilarious effect.

I've posted about this before, I know, but today's entry is about this year's "winners."

Now, you'll have to go to the site to see the Grand Prize Winner. Suffice it to say that I don't agree. It's bad, but not dark-and-stormy-night bad.

I'll do what that site doesn't, which is to first paste the inspiration for the contest, the actual opening line of Paul Clifford (they put it way down the page):

It was a dark and stormy night; the rain fell in torrents—except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.

Now, some of my personal favorites:

It was a dark and stormy night, which makes perfect sense when you realize we’re on Neptune, with a mean distance from the Sun of 4.5 billion kilometers (or 30 astronomical units), and winds that howl at 100 meters per second, composed of mostly hydrogen and helium (and only trace amounts of methane), which is way better than Uranus, which stinks to high heaven.
—Jon A. Bell, Porto, Portugal

Yes, I'd probably have selected that one as the Grand Prize Loser, mostly because I'm sick and tired of seventh-planet puns, but also because of the completely unnecessary science data.

And, of course, I'm quite fond of the Vile Puns section:

"I do enjoy turning a prophet," said Torquemada, as he roasted the heretic seer on a spit.
—A. R. Templeton, Stratford, Canada

And:

"My laddies may not be the fastest sugar cane harvesters," Fergus confessed, "but they're not as slow as my lasses..."
—Mark Meiches, Dallas, TX

Just one more; like I said, the page is there to view the other stinkers at your leisure:

Ralf Smalborgson kept a small shop in Direperil, Minnesota, and his goods consisted only of medieval stringed instruments, lanyards and backstays, and some limited apothecary supplies, giving the store its uninviting signage: Lute, Rope, and Pillage.
—Ciarán McGonagle, Derry, Northern Ireland

Which reminds me of my D&D-adjacent bard, one of whose catchphrases is, "Come on, baby, fight my lyre!"

3 Like • Comment • View 2 comments

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