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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 18 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 18, 2024 at 10:39am

#1075432

Revisited: "Challenge Complete"

Today's cruise on the river of time takes us back to the end of January, 2019. This was a 30 Day Blogging Challenge month, and for context, my current daily blogging streak wouldn't start for another ten and a half months. And, of course, it was before everyone's lives got disrupted.

The entry itself, "Challenge Complete"

, featured the kind of prompt I came to expect for the final entry into that challenge:

Write a list of at least 5 blogging prompts to add to the Challenge War Chest to be used for future rounds of the 30DBC. Then, use one of your own prompts to write your entry.

I've never really enjoyed coming up with prompts. Scratch that; I do enjoy it; it's just that when I'm expected to create one, my mind goes blank. I know this sounds odd from someone who's been judging "The Writer's Cramp"

[13+] and therefore coming up with a prompt almost every week for nearly two decades, but there you have it. I just think of it as another challenge for myself.

The actual prompt list I came up with is uninspiring to me even now, and I won't quote it here. It's there at the link if you want. I'll just address some of the other things I said in the entry.

I don't know who coined the term "bucket list," and I can't be arsed to find out.

Unlike most words and phrases, they've traced that phrase in its "things to do before you die" sense to a precise moment.

I do know that it became the title of a moderately interesting movie with Jack Nicholson and God.

According to that link I just did, the phrase's origin and the movie title came from the same place.

While I've been known to use the phrase from time to time, I usually call it my "fuck-it list." This is because I've already done most of what I set out to do, and have given up on the rest.

Good to see my attitude hasn't changed in five and a half years.

It's come to my attention recently that life is much less frustrating if you can separate "things that I cannot control" from "things that I can control," and to focus on the latter while letting go of the former. This is something akin to the infamous Serenity Prayer, which I resent because a) it's a prayer and b) it's associated with AA, and AA is for quitters.

That's not my actual problem with AA, but it made a decent joke.

I've been walking every day for the past 5 weeks, which is, like, a new record for me for exercise.

I should have kept track of my record for "days without formal exercise." It'd be a lot longer.

Say I want to take a trip to space. How can I make that happen? Well, probably by paying Virgin Galactic a very large sum of money to fire me into a suborbital trajectory that technically takes me 100km up for a fraction of a minute, thus putting me, by definition, in space.

I think that particular venture never took off (pun intended). Branson lofted himself into a suborbital trajectory, but his maximum altitude was somewhat less than the accepted boundary of "space." Pretty sure I wrote about it in here at the time. Then Virgin declared bankruptcy. Or something. I can't keep up with all the rocketing these days.

Honestly, even if I were a billionaire, this would strike me as a colossal waste of money.

While I accept that other people wouldn't find it so, paying any amount of money for fame and bragging rights.

So here's the real example: I want to be published.

Yeah, not so much anymore.

Not much else of note. Kind of a boring entry, even now. Only one joke that I could find, and it wasn't even original.

Can't be "on" all the time, I suppose, but some challenges are never complete until the day you kick the bucket.

1 Like • Comment

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