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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 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

August 11, 2024 at 9:14am

#1075049

Revisited: "It's a Trappist!"

Well, this entry from July of 2020 is embarrassing: "It's a Trappist!"

For starters, it wasn't the first time I'd used that title. In my defense, it's a truly awesome pun combined with a Star Wars reference joke, so I tend to use it a lot.

The entry itself was a response to a 30DBC prompt that went like: "If you won a free trip to any foreign country, all expenses paid in your own private jet and had the time to go (and there were no travel restrictions due to a global pandemic

), what is the first foreign country you would visit? Who would you bring with you? What would you spend your time doing?"

And I think we all know the answers to those questions as of 2024, but four years ago, things were a bit different.

Last year was my mostly-stay-at-home year. Not only did I want to conserve money for upcoming trips, but I wanted to lose weight so I wouldn't look like a typical American.

I was mostly successful at both.

I got even better at conserving money for upcoming trips because I could barely go anywhere for four years. The weight thing, I don't talk about.

The plan was to go to Scotland in May with a friend for the Islay festival.

That might still be my next venture. Obviously, it hasn't happened yet.

This shit will not be resolved by next year. So I doubt I'm going to Belgium or France. Or Scotland. Or the Netherlands. Or Belize. Or even travel in the US.

Oh, but I did end up doing a road trip in the US the following year. That did not end well (though it could have been a lot worse).

I'm prone to depression and this shit is not helping. Not the pandemic, not the travel restrictions caused by the pandemic, and certainly not prompts like this one. The only thing I have to look forward to these days is travel and death, and it looks like the latter is going to happen before the former.

See, this is why I'm a pessimist. Either I'm wrong, which makes me happy, or I'm right, which makes me happy. If I were an optimist, I could only be disappointed by the results.

Even if I somehow manage to stay alive and reasonably healthy (unlikely), my passport will probably expire before I get a chance to travel again. And I haven't even used it since I last renewed.

The major impetus behind planning a Europe trip this year is to use that damn passport before it expires.

But right now? In the utterly impossible scenario above? Belgium. With my friend, as I mentioned, and whoever else wants to go. Primarily, I'm interested in immersing myself, at least figuratively, in Belgian beer. Trappist ales, saisons, whatever. I can get some of them here -- I just had a nice couple of bottles of Delirium Nocturnum yesterday, and there's still one in my fridge along with a big bottle of Kwak -- but as with California and wine, they keep the really good stuff for themselves.

Coincidentally (or not), I have some Delirium Nocturnum in the fridge right now. It's very difficult to find Kwak here.

So the rest of that entry was just responding to the prompt. I'll be traveling alone, and also visiting France, so, not exactly what I had planned (which I don't mind), but dammit, at least it's (probably) going to happen and I can stop annoying everyone with "what I wanna do" posts.

3 Like • Comment • View 2 comments

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