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Sunday, Sep. 8, 2024

9:34pm 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 11 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 27, 2024 at 8:33am

#1074446

Still Planning

Time for a travel plan update, though it's probably going to be short. But maybe I have some other things to write about.

The travel agent I'm going with has a subcontractor for local knowledge. In this case, a French woman. And I'm completely on board with that, but the sub didn't get back to her before Wednesday of this week. And that matters because the agent took off for vacation on Wednesday, so that means no further information until, at least, Thursday of next week. Probably later, because she's the owner of the agency, so she'll be coming back to utter chaos that she'll have to deal with first.

Or, you know, maybe she's a better business owner than I was, and everything will run smoothly in her absence.

Must be nice to go on vacation when you're a travel agent. You can get yourself the best deals.

And there's not much else I can do until I at least know when I'll be leaving, which I don't yet. I tried searching for fun things to do in France, but Google keeps pointing me at the Olympics, and I don't give a shit about that.

Which, it occurred to me, may be hypocritical of me, as I've harped in here again and again about how there's no such thing as useless knowledge or experiences. And I do believe that. My rationale (or at least rationalization to make me feel better about myself) is that I also tend to avoid anything that's too popular. Like Taylor Swift (who I acknowledge has talent) or "reality" shows.

But yeah, I do have an aversion to sports. You know how kids sit bored in math class wondering how they're ever going to use this? You ever notice no one says that about gym class, even though the vast majority of the kids aren't going to go on to be professional athletes? "But, Coach, when will I ever use sit-ups in my career as a veterinary technician?" "Well, um, strong abs will help you lift big dogs onto examining tables."

My argument is that you never know when the stuff they teach you in school will be useful or necessary. Was it "necessary" for me to spend high school in orchestra and drama class, let alone Latin? No, probably not. And I didn't know I was going into engineering until like senior year, so even math was questionable. But I learned all that shit anyway (and promptly forgot most of it).

The point being that just as strong abs are generally a good thing (something even I can acknowledge) even if you're not a pro athlete, so it is with a strong mind.

Now if only schools would emphasize that sort of thing instead of being all about the football team, we might actually get somewhere.

What does this have to do with travel? Well, nothing, except that maybe I can stretch (another good exercise) and claim that travel broadens one's perspective, so it's the same sort of thing. But, mostly, I'm rambling because I didn't accomplish anything else in terms of travel planning this week.

Next week, I'm going to look into relatively cheap laptops so I can bring one on the trip. Like a Chromebook or something, so I don't have to use my phone to make blog entries. I don't want to take my expensive gaming laptop with me (the one I'm typing on now), so this seems like a reasonable thing to do. Besides, it never hurts to have a backup here at home in case this thing blows a circuit one day.

And then I have to see about getting internet there. I'm well aware that they're ahead of the US in that regard, but that doesn't mean the systems are compatible, kind of like how I have a plug adapter to handle the different electrical outlet configurations.

5 Like • Comment • View 4 comments

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