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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

Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 13 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 18 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 19 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

a day ago
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

August 4, 2024 at 10:31am

#1074760

Revisited: "NaNomaterials"

Today's peek into the past takes us back to September of 2018, and discusses a certain novel-writing month: "NaNomaterials"

Ever since I first heard of NaNoWriMo, I've been conflicted.

I'm not really conflicted anymore; I just don't care enough to put in the necessary work.

I don't generally jump on bandwagons. If something becomes popular, I view it with a certain amount of distrust.

What's worse is that there are things I like that are popular. And I absolutely hate it when people assume that I like it because it's popular.

Yeah, I joined Facebook pretty early on, but I'm not active there anymore.

I can't even get into my account long enough to close it.

And the first time I heard about Twitter, someone told me that some guy had rigged his office chair to tweet every time he farted. I swore then I would never be a Twat (or whatever they call people who go to Twitter), and nothing I've heard about Twitter since then has convinced me it's gotten any classier.

Clearly, it's only gotten worse since that entry. It's not Twitter anymore, for starters, but X. Or, as I call it, Xitter (where the X is pronounced like sh). A post on the site is called a Xit (also sh).

And no, this isn't some hipster thing for me. I won't join that group, either.

I was hipster before it was cool. Then I stopped.

There follows a promotion for "October Novel Prep Challenge"

[13+], which I still recommend to anyone planning to do NaNo (or just want some help and motivation in getting a story together).

Anyway, I'm trying to decide whether to attempt it this year. Of the three I've completed, two of them are crying out for sequels (or, really, continuations to make them 100,000 word novels), and I've got a couple of ideas for new ones, though none are very compelling to me.

Here it is six years later, and none of them have been edited yet.

Of the three I've done, one's straight science fiction; one's contemporary fantasy; and the latest is, well, not a serious attempt at getting anything publishable done - it's science fiction erotica. Naturally, that's the one I most want to continue with, and it's the one least likely to get read.

I spent so much effort world-building that last one that I've considered setting more serious fiction in that universe. "Considered" being the key word. The title of the entry was meant to be a pun on a science fiction trope, one which, like much SF, is entering consensus reality.

So why start something new when I can't finish what I've already got going?

On the other hand, if I can't finish what I've already got going, why not start something new?

Not this year, though. I expect to be traveling during October, and recovering during November.

5 Like • Comment

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