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Thursday, May. 23, 2024

12:01pm 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:

Aiva Raine

a day ago
In response to "More Science"

Giggles. Thank you for the laugh- especially this phrase, "I always picture Doc Brown's workshop in Back to the Future. Yes, of course I know it's wrong, but I'd rather be amused than right."

1 Like

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

June 17, 2020 at 12:08am

#985822

Zombie

I ventured Out Into The World for the first time in three months yesterday. Well, unless you count walks to medical offices; I don't because those aren't fun. No, this time, I walked over to the shopping center because I had to pick up a prescription (as a result of one of the trips to the doctor -- not a big deal, just routine), and then I noticed that the nearby taphouse was open for outdoor seating.

It was around 3pm, and the temperature was only around 70F (quite low for a Virginia afternoon in mid-June), so there was no wait. Thus, I was able to have my first (and second, and third) draft beer since mid-March.

It felt almost... normal.

Then I walked home and passed out. And that was definitely normal. Downside to losing weight? Lower tolerance. Upside to losing weight? Cheaper to get drunk.

Anyway, today is entry #5 for "Journalistic Intentions"

[18+]

8. Try not to become a man of Call of Duty prowess, but rather try to become a man of legitimate Zombie Apocalypse fighting skills.
Brandiwyn🎶

I'm not familiar with whatever the original of this twisted quote is. Probably doesn't matter.

Confession time: I've never played Call of Duty. I don't actually know much about it. I'm more of a Bethesda fan: Elder Scrolls, Fallout, that sort of thing. I've heard good things about CoD and its sequels, but just never got the urge to play it.

But I don't think that's the point.

All the joking around we all used to do about the inevitable zombie apocalypse seems rather naive what with everything going on right now. An actual pandemic? Cops out of control in the streets? Yeah, no thanks. The attraction of fantasizing about a zombie apocalypse was that the line between the good guys and the bad guys was really clear. Good guys: not zombies. Bad guys: brain-munching shamblers. You could project all of your hate, fear (they are not the same thing), and prejudice onto the hordes of moldy undead.

Liberal or conservative, warmonger or peacenik, we could all agree that zombies are bad and need to be eliminated. They are, however fictional, the Common Enemy, and (with a few exceptions in movies and whatnot) there's no nuance there. The survivors have to band together, cooperating against an all-encompassing threat.

Even when you have the whole space-alien-invasion trope, there's always, somewhere in the background, the idea that some people will side with the aliens. Not so with zombies. We're all in this together.

Well, recent events have thrown into sharp focus the realization that we're not all in this together, and probably never will be.

So, give me a video game. Preferably one where I can play as a good guy, or as a bad guy, or (my favorite) a bad guy who convinces everyone he's a good guy. Escape from reality? Sure. Have you seen reality?

Three very interesting and well-written answers to yesterday's mini-contest about Why We Are Huge. Though I do have to say I'm just a little bit disappointed that no one proposed "space aliens are fattening us up for the harvest."

So it's close, but this time the MB goes to SB Musing

. Check yesterday's comments for the post; it's too long to comfortably copy/paste here. Thanks for reading and commenting!

I'll try this again sometime soon, though probably with some subject matter that's a little less... weighty.

9 Like • Comment • View 8 comments

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