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Saturday, Dec. 21, 2024

10:52am 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:

tj-Merry Mischief Maker

about 17 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 22 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 22 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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

July 28, 2024 at 9:39am

#1074494

Revisited: "The Truth is Out There"

In another astounding coincidence, the random entry I picked to revisit today, from April of 2020, touches on many of the same topics I discussed last week: the search for alien life, and science in general: "The Truth is Out There"

Hell, it even has a similar title to last Wednesday's entry. Look, I'm closing in on 2800 entries here; I'll get there before August is out. I know some titles have been repeated. Sometimes, I make an effort to avoid reusing a title, but much of the time, I can't be arsed. This isn't even a case of reuse, but variation on a theme.

In any case, I consider last Wednesday's entry to be the update on my opinion on the subject of the search for extraterrestrial life, so I'll try to focus on other things I wrote back then.

I've been following this guy, PZ Myers, for a while now, and while I don't always agree, I appreciate his point of view. Except about movies.

I think I've linked his blog at least once again since then. Still reading his stuff, though he's become utterly obsessed with spiders. I don't hate or fear spiders, but I lack that level of obsession. That's not the only thing he posts. And I've grown to appreciate his point of view about movies, to the extent that he's a negative barometer for me: generally, if he hates a movie, I'll like it, and vice-versa. Especially when it comes to comic book adaptations. Just recently, he ragged on the Deadpool/Wolverine movie, which served to make me want to watch it more. Which I haven't, yet.

Thanks, Myers, you made me look up a word for the first time in years.

The word then was "apophenia." Since then, I've discovered even more words I had to look up (not counting those I chose to look up due to my interest in etymology, which is not the same thing as an interest in entomology, which doesn't include spiders). I count any day when I learn something new as a good day. Well, unless something bad happens to balance it out.

Pretty much everything else is either not noteworthy, or was covered in here last week. Except for a big fucking oops on my part, where I apparently pasted a quotation twice. I try to do some basic proofreading before I post these things, but sometimes, something slips through the process. Still not as bad as when I find a years-old typo. Those are truly embarrassing.

But hey, at least that's evidence that I don't post using Artificial Intelligence; anything I put here is either a quote or Natural Stupidity.

3 Like • Comment • View 1 comment

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