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Saturday, Nov. 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:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

November 26, 2021 at 12:02am

#1022331

Busted

Well, its been a while since I've done a free-form entry.

PROMPT November 26^th

Today is Thanksgiving here in the United States. I know this is the prompt for tomorrow, but I'm going to give you something to be thankful for. The prompt for tonight is to be yourself. Write whatever is on your mind. Provide your own prompt, so-to-speak. I look forward to reading your posts!

I woke up Thanksgiving morning to find a fraud alert on my principal credit card.

Apparently someone had gotten my digits and paid their utility bill, signed up for Apple Pay (I'm an Android user), and racked up hundreds of dollars in charges at Carhartt's and some place called Ice Bling (which cracked me up). All in the space of less than 24 hours.

Nothing to be thankful for, right? Well...

This is why I use a credit card and not a debit card.

Quick call to the issuing bank, five-minute hold time -- and not a single one of those charges are my responsibility. Debit cards just don't provide the same level of protection (if there are any out there that do, I'm not aware of them). And you might not think it'll happen to you, but it will, eventually -- someone will skim off a gas pump (not what happened here because I don't use that card for gas and anyway, I haven't bought any since July), or a waiter will help themselves to an extra tip, or there's a website breach somewhere. Doesn't matter how. So this is where my optimistic cynicism comes in: I take precautions, but I also expect them to fail at some point, so I have plans for when that happens.

There is a measure of inconvenience involved. It won't be until sometime next week before I get the new card, with a new account number and whatnot, in the mail, so I get to go the entirety of Buy Shit Weekend without my main credit card. Whatever; I don't buy much anyway, and besides, I have other credit cards for precisely this reason (and also because some of them offer extra rewards for certain types of purchases).

I will also have to change all of the accounts that autodraw from it, like Uber and Netflix. Pain in the ass, but it's not like I had anything else planned for the weekend.

"But Waltz, don't you pay more in interest charges than you get in cash back?" Well, no, see, if you treat your credit card like a debit card, never spending more than you have cash to cover it, and pay the balance in full every month, turns out they don't charge interest. I haven't paid a penny in interest or fees on a credit card in decades; rather, they pay me.

I mentioned sometime last month how I feel about thieves. They all suck (and that includes the banks with the interest some of them charge people who don't pay their balances in full). And in this case, who eats the fraudulent charges? The issuing bank or the CC company, I don't remember which. They expect this to happen, so they charge merchants accordingly. In the end we all pay, so yeah, fuck that thief, but it doesn't directly affect me.

So all in all, nothing more than a minor inconvenience. Therefore, don't mistake this for a plea for sympathy or a complaint; it's just that nothing else of note happened yesterday and I thought I'd point out exactly why credit cards are better than debit cards, if they're used properly.

One other thing I did yesterday was go see a movie, as I'd planned. So here's a review.

One-Sentence Movie Review: Ghostbusters: Afterlife:

Although this movie won't make a lot of sense if you're not a fan of the original Ghostbusters, I think the three people who aren't won't bother with this one, anyway; and while I'm glad I saw it in the theater and parts of it are a lot of fun, the movie suffers from several missteps in pacing and editing, with some real head-scratcher shortcuts.

Rating: 3/5

6 Like • Comment • View 10 comments

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