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Saturday, Dec. 21, 2024

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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

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10 Most Recent Blog Comments:

Annette

19 minutes 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

about 18 hours 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

about 23 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

about 23 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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 24, 2024 at 9:03am

#1077221

All Out of Louvre

So, yeah, I didn't go to the Louvre yesterday.

Look. I'm not a young man of 55 anymore. Sometimes, my knee hurts. Yesterday was one of those times, because I'd spent the last two days hiking around Paris.

Paris was never the purpose of my trip. I agreed to three days there because I figured I could use the time to get over any jet lag, and see firsthand how bad my French pronunciation is [Narrator: vraiment très mauvais], and also to meet my new friend there. No, the purpose of the trip was wine tasting in the countryside, and beer drinking in Belgium later.

If I'd gone to the Louvre, that would have been more walking and standing and stopping and staring. I would have liked to have seen some of the art, of course. But not the Mona Lisa. There's only one reason to see the Mona Lisa, and that's to be able to brag that you've seen it, while complaining about how small it is and how crowded with tourists the room is. The obvious hypocrisy there is that you're contributing to said crowds.

I can skip the seeing it bit and accept the information that the painting is surprisingly small and the room is extremely crowded.

Besides, if I can't paint a mustache on it, what's the point?

So, in an effort to preserve my walking ability for the really important stuff (chateaux and wineries and such), I kept things pretty low-key yesterday while my knee recovered. But I did get a bit of walking in. For instance:

Remember how I said most French beer is ass, except for some breweries in the east? One of those breweries produces a lager called 1664. It's a fairly large brewery that exports, so we get bottles back home. I've heard it's pretty popular in England, too. I buy it to drink when I want a lager, because it's a better alternative for that style than the pisswater the big names try to pass off as lager. Anyway, I found it on tap at a restaurant near the hotel, so of course I ordered one, and it was even more delicious than the bottled and exported version.

And also, if I'd wasted the day at the Louvre, I never would have encountered this delightful example of street art:

7 Like • Comment • View 4 comments

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