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Monday, Jul. 8, 2024

1:04pm 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:

Elycia Lee ☮

about 3 hours ago
In response to "Playing Chicken"

But it is far more interesting if it is categorized as 'culinary conspiracy'.

2 Like

Elisa: Middle Aged Stik

a day ago
In response to "Revisited: "The End is Nigh""

I feel like the newsfeed came along some time between 2010 and 2012. I know that time involved a major site redesign that had people in a major tizzy. They thought that WDC was trying to become a social network. If you ask some people, that kinda ended up happening. It accelerated a trend I noticed so long ago that I made a poll about it: "Status Versus Merit"

[E]. Hey, wait a minute. That poll was inspired by events in 2007. oincidence? Maybe, maybe not.

1 Like

Kåre Enga in Montana

Jul 6, 2024 at 12:16pm
In response to "Down in the Valley"

I would like to get to the Loire. There's plenty to see so I'd just take it slow, a saunter instead of a march, a Rêverie (think Debussy).

There's quite a lot on youtube but I don't have time to get lost today.

When you are there... get lost.

1 Like

Kåre Enga in Montana

Jul 5, 2024 at 6:28pm
In response to "It's Called 'Fiction' For a Reason"

For us older folks, Sweet Child*, "Leave it to Beaver" was the ideal... unfortunately, that ideal existed for very few people. And for many it was never their "American Dream".

*anyone younger than me is a 'child'.

Wordsmitty ✍️

Jul 5, 2024 at 1:19pm
In response to "It's Called 'Fiction' For a Reason"

"cars inevitably explode when run off cliffs." Has anyone seen the "Myth Busters" episode of running cars off cliff to see if they explode? Well, there's your answer.

1 Like

Elisa: Middle Aged Stik

Jul 5, 2024 at 9:37am
In response to "It's Called 'Fiction' For a Reason"

"in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford."

Given Redford's politics, some people might consider this a utopia.

"Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA."

I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record.

2 Like

tj ~ endeavors to persevere!

Jul 5, 2024 at 9:09am
In response to "It's Called 'Fiction' For a Reason"

Great post. It seems now it's not ideas from movies as much as, "I seen it on YouTube, so it must be true", or at least that's been my observation.

2 Like

🌕 HuntersMoon

Jul 3, 2024 at 10:12am
In response to "A Bridge Too Far"

Just my opinion but I think he's lost his crown by being out-swindled by an even larger-than-life conman. Still a New Yorker, however, so the city still retains its reputation.

1 Like

tracker

Jul 2, 2024 at 9:08am
In response to "Imma Let You Finish, But..."

I am a sports fanatic!!!! You will see more of me.

1 Like

tj ~ endeavors to persevere!

Jun 30, 2024 at 11:01pm
In response to "Revisited: "Rock you like a...""

I also purchased a generator because our power would go out anytime the wind blew. It seems to have worked, we seldom have power outages now. Living in Minnesota, all we get when the hurricanes push threw are thunder storms and rain. But, it's Minnesota, so thunder storms and rain are normal. This year does seem to be rainier, however.

I'm thinking, after reading this, that I should invest in a couple of rain barrels and bottle the water up. I could probably sell it online to drought stricken people.

1 Like

July 5, 2024 at 8:05am

#1073565

It's Called 'Fiction' For a Reason

It should be well-known by now that one shouldn't get one's facts from comedy sites like Cracked. Especially when that source tells us we shouldn't be getting our facts from movies, either.

5 Universal Beliefs That We Got Thanks to One Single Movie

If you see something in enough movies, you assume it’s true. If every movie has bears growling or frogs ribbiting or vampires hating lemons, we assume that’s how the real world works, because movies are the only form of education we have.

For instance, thanks to movies, I know that cars inevitably explode when run off cliffs.

Sometimes, however, no trend is necessary. All it takes is one influential movie...

Kind of like how the documentary Willy Wonka and the Chocolate Factory taught me how candy gets made.

5 Presidents Are Supposed to Wear Flag Pins

A few years ago, a friend of mine got married. The bride asked me to be her Dude of Honor, so I had to buy a suit. The suit came with a flag lapel pin.

I didn't wear the pin to the wedding. Too political.

You might even say a president wearing a flag pin is redundant, since he’s already the president and his nationality isn’t in question.

Oh, how quickly we forget.

The first president to wear the pin was Richard Nixon, and his staff convinced him to adopt it after watching a 1972 Robert Redford movie called The Candidate.

So, to be clear, the clowns we have in office these days all emulate a disgraced former president, who in turn got the idea from typical Hollywood bullshit.

This explains a lot.

As for Redford, a few years after The Candidate, he starred in All the President's Men, a movie we trust Nixon enjoyed just as much.

Ooooooh, sick burn.

One final amusing note: in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford. Imagine that, an actor as President.

4 Pirates Used the Pirate Accent

We have this concept of “pirate speak,” of a single accent that pirates use. The more pirate-y the pirate, the closer they’ll adhere to this accent... Our idea of the pirate accent comes entirely from one actor, Robert Newton, and his performance in 1950’s Treasure Island.

Eh, doesn't matter. It's iconic at this point. Arrr. Shiver me timbers.

3 Rabbits Like Carrots

We all associate rabbits with carrots, but the two don’t go together naturally at all. The carrots we eat don’t exist in nature at all, as they’re the result of a whole lot of selective breeding.

Otherwise known as genetic modification.

Rabbit like greens, and they can eat the leafy top of a carrot, but if a rabbit gorges itself on carrots, that’d be like you trying to live on cotton candy.

Or on rabbit meat, for that matter.

Of course, Bugs Bunny wasn't a movie star at the time, but as the article notes, he was emulating Clark Gable.

2 Mohawks Wear Mohawks

The mohawk is a hairstyle. It’s also a name for an indigenous people from the eastern United States, so you probably think that hairstyle is named after the people.

Gosh... Hollywood getting Native American culture wrong. Who could have expected that?

1 Rockets Should Count Down to Takeoff

Except that there's sound reasons for a lot of the countdown. Rockets are somewhat intricate and complicated machines (hence the equating of "rocket scientist" with "genius,") and their launch preparations require a checklist of things to be done in a precise order at precise times. Not that I know anything about it, though; I'm not exactly a rocket surgeon.

NASA got the idea of counting down to launches from a German film called Woman in the Moon. This Fritz Lang silent picture was the first ever big-screen depiction of rocket travel — Georges Méliès’ earlier A Trip to the Moon was a far less serious look at lunar travel.

The Méliès film (itself a Verne adaptation) is the one with the absolutely iconic image of a space capsule getting in the eye

of the Man in the Moon.

Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA.

Countdowns really are thrilling. Just look at this very article. It could have counted up from one to five, and newcomers to this site may be baffled at why it doesn’t. “Is this a ranking from five to one?” they might ask. It’s not.

Anyone here not expect the self-referential humor? I certainly did.

6 Like • Comment • View 4 comments

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