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Sunday, Dec. 22, 2024

11:43am EST

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Complex Numbers

by Waltz Invictus

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:

Annette

about 24 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

September 30, 2024 at 3:01am

#1077469

Owl Miss This Place

For my final full day in Dijon, I didn't have anything planned out—no wine tours, no mustard discoveries, not even a "let's meet for lunch" (because unlike Paris and, by lucky chance, Tours, I don't know anyone here). So, as the day was fine and sunny and neither hot nor cold, I took a walk.

Dijon, like most European cities, is really quite incredibly old (from a US perspective). And, as with other cities, there's only so much one can do in a day. Turns out that Dijon has a self-guided walking tour embedded into it. Literally; there are brass plaques with engraved owls

on the sidewalks, pointing the way.

Why an owl? Well, on the side of the cathedral here (also named Notre Dame, because Catholics weren't very original) perches a small stone owl, barely recognizable as such from the accumulated wear of people touching it. Supposedly, touching it (but only with one's left hand) will grant a wish. Apparently, no one has yet wished for "restore the Notre Dame owl to its original carved glory." Or maybe they have, and it's just another silly superstition.

Following the trail eventually gets you to the owl, and then it moseys on along through other historic sites. It's like following the quest markers in a video game, which made me want to play a video game, but that can wait until I get home again.

I didn't touch the owl. For one thing, it's a silly (if mostly harmless to everything but the owl itself) superstition. For another, even if there were something to it, making a wish is tantamount to acknowledging that there's something missing in my life, and there isn't. For yet another, over half a century of reading and writing stories, and playing fantasy role-playing games, has instilled in me a deep, abiding distrust of wishes. And, for a final thing, some beggars were approaching with their cups out, so I hoofed it out of there, continuing to follow the brass owl arrows.

These led me next to a mustard shop, on the same street (Rue de la Chouette, naturally), where I finally got to see the thing Dijon is most famous for and holy condiments, Batman, there's a lot of mustard there.

At some point, though, around the Ducal Palace, I lost the trail and never did pick it up again, despite looking and even trying the internet. All I could discover was that it was not, in fact, the end of the trail. Oh, well.

Much later, in the evening, I returned to the palace area (Palais des Ducs) and its accompanying semicircular courtyard, Place de la Libération, which is surrounded by cafés, bistrots, restaurants, bars, and brasseries, the differences between which are subtle and very French. (Brasserie also means "brewery," but not all brasseries are actually breweries, much to my disappointment.)

Point is, I went back there for dinner because it's pretty, and I sat outside with a beer and a burger as the sun set and the Palais des Ducs lit up, and the shifting, multicolored lights in the Place's fountains illuminated their waters.

This sort of thing is one of the reasons I wanted to go to France.

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