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Sunday, Sep. 8, 2024

9:24pm EDT

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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:

Elisa: Middle Aged Stik

about 9 hours ago
In response to "Writing It Off"

I am late to the party with my comments, but here we go.

Used to be, I wanted to get published.

I used to want to be published in terms of stories. Nowadays I'd rather be published in terms of photos. And self publishing may be my only option in that regard.

but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

And before that it was crowded with middle aged socialites with nothing better to do (but did have some level of writing skill).

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay.

I admit that as of late I don't let my book items hit the entry limit. Part of it is my entries are super long (current average being *checks notes* 7.48 kb in size). Part of it is I also feel like book items should end after at most five years. I think of my old paper diaries and how they felt more meaningful when I didn't let their use drag on forever. If I stayed consistent, they'd end maybe at most after a year and a half. They often wrapped up sooner than that. Even moving to online journaling, I appreciate a journal that is finite not based on the number of entries but by time elapsed since the book started having entries added to it. My current journal may last a tad longer than my previous ones, but I imagine I'll wrap it up in late 2027, maybe early 2028. We'll see how much space I have to work with. In the old days, 1000 entries was considered a major achievement of an end point. I hope I can get that much out of it, as I think that's more reasonable. I do think 3000 entries of my kind of work in one place is a bit much.

1 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Revisited: "Orange You Glad This Wasn't You?""

Maybe this would help... or at least attract your attention?

1 Like

Robert Waltz

about 22 hours ago
In response to "Spit in the Ocean"

Both commenters today had already received MBs from me this week, so I went back to every entry this week and picked a comment at random.

The final Birthday Week MB goes to:

🌕 HuntersMoon

Thanks, everyone, for reading and participating!

1 Like

Robert Waltz

a day ago
In response to "Spit in the Ocean"

Wordsmitty ✍️

- we do have a micro-bakery here. Well, they don't call it that. But they sell great cookies. And bread.

1 Like

Wordsmitty ✍️

a day ago
In response to "Spit in the Ocean"

The best way to improve the world is to start small, such as supporting local, small businesses, like a micro brewery. Even if it tastes bad, help improve it by telling them that they're selling shit (or burn it down). Damn right that will make the world better. I just wish wish there were more micro bakeries making cookies.

Robert Waltz

a day ago
In response to "Spit in the Ocean"

That's definitely a good point, Elisa: Middle Aged Stik

, and honestly, a lot depends on my mood. I was in a foul one this morning due to lousy sleep.

Still too lazy to actually do anything that would inconvenience me, but at least I'm not as bitter about it now, all these hours later.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Spit in the Ocean"

Yes, I can do all these things.

But I won't.

Are you sure you want that kind of nihilism to be contagious? If so, you run the risk of of those big systemic changes not happening. Let's be real. We are a component of these systems whether we like it or not. Shifting to pinning blame on a faceless entity without also modifying our behavior entrenches the status quo.

1 Like

Robert Waltz

a day ago
In response to "Secretion"

One comment, automatic winner! Jellyfish~Happy Birthday WDC

, your MB is on the way.

Tomorrow: last chance at Birthday Week Merit Badge!

1 Like

Jellyfish~Happy Birthday WDC

Sep 6, 2024 at 4:21am
In response to "Secretion"

Had to have a look at other people's entries as I just looked at the prompt and thought the same thing - errr - No! Now what can I write? I have come this far with the blogging challenge I don't want to give up now. I like the way you have come up with an answer - very clever and no I had never wondered that but interesting!

1 Like

Robert Waltz

Sep 5, 2024 at 11:35pm
In response to "Writing It Off"

Thank you all for your comments and suggestions!

The randomly selected winner of today's Birthday Week Merit Badge is...

(dieroll, please...)

Jayne

I'll send that out shortly. Another chance tomorrow!

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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