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Tuesday, Apr. 16, 2024

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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 the Bunny Stik

a day ago
In response to "That's Cole"

"I don't know what the latest fad food is, but I can almost guarantee that behind the fad is someone with money trying to make more of it."

I'd say there are multiple fad foods, including goji berries. That said, cauliflower became trendy in 2018 and has maintained some level of staying power. I still see cauliflower rice as an option in many places across the US.

4 Like

Elisa the Bunny Stik

Apr 13, 2024 at 6:10am
In response to "Mawwiage..."

"Or, at the very least, it's an emotional bond more than a business arrangement."

And for a substantial subset of parents, it's neither. They either just want kids to show off like trophies or dive headfirst into various forms of abuse.

3 Like

Aennaytte: Free & Wild in GoT

Apr 12, 2024 at 12:39pm
In response to "Coincidences"

Some words even cross species.

My golden cat calls me Mom frequently.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:58pm
In response to "A Cinderella Story"

Do you mean something like Carl having to work in the garage for his wicked step-dad while his brothers party? He was polishing an old hubcap that was magical and the next thing he meets a rich cougar at the club but has to leave by midnight when the spell wears off. As he exits he looses a boot. The cougar takes the boot with her and ends up having car problems the following day and stops at the garage where she notices Carl sweeping the floor with only one boot. She hands him the boot, it fits, and they are last seen sailing off on her yacht.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:48pm
In response to "Things Go Better With Cahokia"

I bet they left because there wasn't anymore deer to barbecue.

2 Like

Robert Waltz

Apr 10, 2024 at 11:05am
In response to "Dark Side of the Moon"

⭐️Jellyfish⭐️

: Also known as a swag bag, but I usually prefer alliteration to rhyme (and also, since I pretend to be a writer, I like coming up with my own terms). No idea what you call them on that side of the pond. It's not technically "bling" because there wasn't any personal decoration, but it had things like certified sun-gazer glasses, a copy of their special eclipse bottle label art, a winery-logo corkscrew, and some delicious truffles (the chocolate kind, not the mushroom kind). Kind of like a Christmas stocking, but in April and for wine and astronomy nerds.

⭐️Jellyfish⭐️

Apr 10, 2024 at 8:18am
In response to "Dark Side of the Moon"

Wine, an Eclipse, and Pink Floyd Playing - Literally sounds like a Perfect Day!

And A Bling Bag! (Although not sure what this is, I am thinking a bag full of sparkly jewellery which it probably isn't)

1 Like

Kåre Enga in Udon Thani

Apr 10, 2024 at 1:34am
In response to "Dark Side of the Moon"

It's nice you took time out from you routine life and routine blogs. Mind you, routine has some appeal.

I saw the eclipse in 2017 in Montana. I'll probably not see another. Do I care? Well... if I happen to be near one... sure. I missed the lunar eclipse last year in Thailand and I wasn't happy... but I saw one in Venice (even saw Mars).

I agree that a sports venue has an ambience that one loses at an impersonal distance. I was in Allen Fieldhouse when Kansas won the national basketball championship in 2007. Not the same as being at the game, but close. 10,000 fans created some ambience. And the town afterwards? Incredible!

Video is visual/audio at best. But what is the smell, the touch of a breeze, a hot dog or the taste of wine on the lips? Also... one only sees/hears what others see/hear. I want to have my own experience.

Songkran is soon, in three days. I dread it in some ways, but it may be a break from the ennui of hot at night and worse by day.

1 Like

Kåre Enga in Udon Thani

Apr 10, 2024 at 1:20am
In response to "Louisville Sluggard"

I'm very light sensitive...

I don't see much under $100/night and very little over 8.0 that I can afford. Most of the nice places are around $200/night ... or ... what I pay for one month's rent here in Udon Thani.

Why don't I travel the US? 1. Don't have a car. 2. Can't afford it.

1 Like

Elisa the Bunny Stik

Apr 9, 2024 at 9:23pm
In response to "Dark Side of the Moon"

Meanwhile, when I'm back home, I will be yammering on about this subject till the cows come home. I am hoping that this will be my first one.

1 Like

November 18, 2022 at 12:02am

#1040776

Play It Where It Lies

Hell of a hazard.

A Woman Was Caught Whacking a Golf Ball into the Grand Canyon, and the Feds Aren’t Happy
The latest story of a tourist behaving badly in a national park is a real head scratcher

Source is (shudder) Outside magazine. I still don't know why I keep reading their stuff.

Somewhere in the dark recesses of my memories lives my long-forgotten teenager sensibilities. This is the version of myself that delighted in immature pranks, like toilet papering a classmate’s cottonwood trees and playing ding-dong ditch.

Both of which are annoying but relatively harmless. If no one was injured, a school wasn't evacuated, and nothing caught on fire, you were a goody-two-shoes.

I'm not admitting to anything, by the way. Just saying.

I’ll admit it: my teenaged self would absolutely understand the allure of whacking a golf ball off of the side of the Grand Canyon and watching it disappear into the chasm below.

Okay, so true story: they taught us the basics of golf in sophomore gym class in high school. As I recall, we split up into pairs and each pair got a golf club (don't ask me what its number was or whether it was iron or wood) and a wiffle ball the size of a regulation golf ball. The idea was to learn our swings and recover the ball easily.

I was paired up with the class stoner, who, with a level of perception and intelligence only displayed by a high school stoner, found the one real ball in the box of wiffles. One of each pair of students teed up, and on the coach's command, wound up and swung.

Everyone else's ball caught a bit of air and then dropped down to bounce sadly on the grass. Ours, however, made a perfect golf-ball arc through the air and ended up 300 yards downrange.

Coach got up in our faces. "WAS THAT A REAL BALL?"

Stoner nodded. (Like anyone could have done that with a wiffle.)

"YOU GO GET THAT RIGHT NOW."

So we trudged through the bushes. As soon as we were out of sight, my teammate produced a joint from his pocket and sparked it.

Like I said, perceptive and intelligent.

As I recall, we did find the ball, and both got lousy grades in that gym class. Which was the only class my parents didn't care what grade I got in, so it all worked out for everyone involved. Coach got to get in someone's face; stoner got to get high in class; and I got a story.

Anyway. The relevant thing is that, while I certainly got up to some shady shit in high school, I don't think I ever considered whacking a golf ball off the rim of the Grand Canyon. For one thing, it's 2100 miles away. For another, I don't play golf (it generally requires being *shudder* outside).

On Thursday, National Park Service officials posted an update on the Grand Canyon’s official Facebook page about a woman who filmed herself hitting a golf ball into the canyon, which she then uploaded to TikTok. In the video, the woman also loses the grip on a golf club and flings it off the cliffside.

If it wasn't recorded and posted on social media, it didn't happen.

Now, look. The problem with lofting a golf ball into the Grand Canyon isn't that it might hit someone. The chance of that is infinitesimally small, though admittedly if it did happen the consequences would be terrible. No, it's that it might inspire other people to do it. TokTik trends are a thing, and I can definitely see the "Grand Canyon Hole In One Challenge" going viral. With that many balls flying through the air, the chance of hitting someone increases significantly... as does the amount of litter, which is the real problem here. (The article does mention all this later).

Officials acted swiftly, and with the help of the general public, were able to track down the woman.

Snitches.

At Outside, we come across a litany of stories of people behaving badly in the outdoors, and this year has been a busy one.

More reasons not to go into the outdoors.

There were the high schoolers who booted a football off of Colorado’s Uncompaghre Peak...

Touchdown!

...the dudes who were photographed scrawling graffiti in chalk on a rock at the Grand Canyon...

At least it was chalk and not spray paint?

...and the never-ending march of tourists getting too close to animals at Yellowstone National Park.

Those, I have mixed feelings about. I mean, it might injure the poor animal if it attacks and kills the stupid human, but other than that, it only harms the stupid human. So while it's true that one shouldn't get cuddly with a Yellowstone grizzly, bison, unicorn, or whatever they have out there in the wilderness, the penalty is built right in.

Article doesn't mention my favorite Yellowstone idiocy, which is people who see the pretty pools of azure water and decide to go off the very clearly marked trail festooned with danger signs and warnings (you can't tell me what to do! mah freedumz! stoopid government!) to take a dip. Some of those pools are near boiling and have a pH of like 1.5. Here's someone

of whom nothing was left but a foot.

I mean, that sort of thing is just par for the course.

3 Like • Comment • View 1 comment

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