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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

September 26, 2024 at 3:45am

#1077301

Two Castles and a Cave

My schedule yesterday was pretty much: go on a tour.

Now, I've been trying really, really hard not to make a joke about Tours tours. You have no idea how difficult that is for me. It's sitting right there; how can I not pick it up?

I've been unable to find a reliable etymology for the city's name, for which, incidentally, the s is silent. Wiki says there's a "popular folk etymology" that it's named after a Roman named Turonus, nephew of Brutus (but not that Brutus). I've long thought that it comes from the French word that translates as "tower" in English, as in La Tour Eiffel. Far as I can tell, though, there aren't any significant towers here. Perhaps there were, once. Hell if I know.

The point is, I'm trying really, really hard not to make a pun about it.

What I do know is that it's wine country. Pretty much everyone has heard of Bordeaux to the west and Burgundy to the east, as well as Champagne, which is located between Paris and Belgium. I think the Loire valley, or Val de Loire, is not quite as well-known internationally, though it absolutely should be.

Getting back to what I originally set out to write, the travel agent had arranged a small group tour to run outside the city. By "small group," I mean there ended up being three of us. Continuing my run of coincidences, the other two were a couple from Fairfax, in northern Virginia. The guide was this small French woman who'd prepared an entire booklet of illustrations, some quite amusing.

First stop: Château de Chenonceau. I'd never heard of it before this trip, but apparently it's the second most visited castle in France, after Versailles. The really interesting thing about it is that it straddles a river.

Like, the brief version is: someone built a castle on the bank of the river Cher. Later, wanting an easy way to get to the other bank, they built a bridge from the castle to the other side of the river. And still later, a massive three-story structure got built atop the bridge. The day was rainy and nasty, and I didn't get any really good pics of the outside, but you can see the bridge-castle here.

I was starting to gain an understanding of what might have led the French peasants to revolt in the 18th century.

Then we went to a cave.

Not just any cave, of course, but a wine cave. And yes, of course, a wine tasting was involved, complete with a brief tasting class led by a sommelier who supposedly passed on some of the "secrets" of his profession. I mean, they're not secrets anymore, now that I know them. What are they? I'm not telling.

After eating lunch (with wine) just outside the cave, we went on to the next castle: Chambord.

Sadly, it had nothing to do with the berry liqueur called Chambord. Or, really, with any booze. It was another example of the excesses of the French nobility, further deepening my understanding of why the guillotine was invented.

Still raining (which the sommelier had assured us was a Really Bad Thing for this year's grape harvest, because apparently it hardly ever rains in the Val de Loire in early autumn, and I didn't point out that this was probably my fault because I've been known to end droughts in California just by visiting the place), so again, none of my photos are very good and I'll defer once again to Wikipedia.

So, with all the crappy weather, what pic from this tour can I share? Oh, I know! This dude was hanging out in a stable at Château de Chambord. You might need to enlarge it, but I promise the white streak on the right side belongs to a horse.

6 Like • Comment • View 3 comments

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