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Tuesday, Apr. 30, 2024

2:31pm 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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

September 30, 2021 at 12:03am

#1018365

Wake Up Now

It's the final day of September, so I thought I'd take a break from trolling internet articles to do some personal updates and plug a few friends. Er, I mean, plug a few friends' items here on WDC.

Home Ownership

By which I mean, the continuing process of being owned by a home.

Last week, in "Hard, Erect Deck"

, I detailed some of the tribulations involved in replacing my house's back deck. Basically, I'd put it off as long as I could, but the old one was about ready to fall over, most likely with me on it, so this was much-needed home maintenance. However necessary it was, though, neither I nor the cats took kindly to the change. Now, though, it's about half done, with the entire superstructure in place; they still have to do some electrical work to put in some lights and outdoor outlets, and finish up the drainage system. But here I am, tonight, sitting on the new deck getting cancer from the treated lumber fumes.

It rained some last night, and I took great pleasure in being able to stand, dry, on the patio beneath and watch the drainage system in action. Said pleasure was mitigated somewhat by watching the trees in the backyard sway in the thunderstorm's stiff breeze. I don't want one of those trees to fall onto the brand-new deck (or, you know, my house) in the next windstorm, so I guess my next project is to cut down some trees. Let me rephrase that: my next project is to pay someone to cut down some trees (the ones in question are nearly dead anyway).

The only downside to the new deck is that my cats were accustomed to leaping up to the old one from down below. They can't do that now because the new railing is too dense for even a cat to get through. Something about building code changes. I told the contractor this yesterday, and he volunteered to use some scraps to put a cat ledge on the outside so they can jump to that, and thence onto the rail. He also reduced the price somewhat as lumber prices have come down since we signed the contract. I like this guy so far and will probably hire him for other work; sadly, he doesn't do trees.

Meanwhile, some pipes broke in the house so now I have to deal with plumbing issues as well. It never rains but it pours. In this case, it pours discharge from the dishwasher through a cracked pipe. So I also have to clean up that mess. Fortunately, I got the worst of it fixed yesterday, so at least I can run the dishwasher.

Bite Me

Went to the dentist yesterday for a routine cleaning. He found work he says needs done. I was like, how much. They showed me. I nearly had another heart attack. Which would be expensive and probably fatal, but at least then I wouldn't have to take out a mortgage to get my dental work redone.

Transportation

I still don't have a car. I can walk most places or, as I did today to go to the dentist across town, summon an Uber. Two things need to happen before I buy a new car. One, they need to fix supply chain issues so I'm not paying more for the car than I did for the deck. And two, even though I can see just fine for now with glasses, I want to wait for after the cataract surgery. Which leads me to...

If Looks Could Kill

I have an appointment with the eye surgeon late in October. Unfortunately -- or fortunately, if you're as phobic as I am about shit touching your eyeballs -- it's not for the actual surgery, but for a pre-op consultation and verification that I indeed have cataracts. My vision continues to deteriorate, so it's a race to find out if I'll still be able to see a goddamn thing when they finally schedule the surgery. If I quit writing in here, it's because I lost the race.

Don't get old. It sucks. And it's expensive as fuck. One star, do not recommend. Yes, I know what the alternative is; my recommendation stands.

Le Français

On the plus side, I'm still doing French lessons every day. I have a hell of a streak going on Duolingo. One of my Uber drivers yesterday was from Paris. Fortunately, I didn't find this out until after the ride was over (he had an accent, but I didn't peg it as French at the time) and I went to tip him in the app. This is fortunate because I managed to avoid embarrassing myself by attempting to pronounce words in French in front of him, which surely would have resulted in him giving me a one-star rider rating, if not blackballing me from the app altogether.

I said I'm learning. I didn't say I was any good at it. Like I said, getting old sucks.

Movies

I know I haven't done a one-sentence movie review in a while. That's because I haven't been to the movies in a couple of weeks. That, in turn, is because nothing's appealed to me. This should change next month. Provided I can still see the screen.

Some of my blog entries next month, assuming I don't go blind first, will be for:

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts February 1!
#2213121 by Elisa the Bunny Stik

There's still space for other contestants, and I never win that one so don't be all like "I'm not entering a contest Waltz is in." What? You weren't all like that? Okay, cool. So enter.

You know what October means. Halloween shit everywhere. Creative October-themed WDC handles. Pumpkin spice everything. No more Green Day for another year, because September's done ended already. Christmas bullshit appearing in stores, if it hasn't already. Leaves falling off the damn trees for me to rake. And, of course, preparing for NaNoWriMo:

FORUM

October Novel Prep Challenge

(13+)
2023 Sign-ups are CLOSED. A month-long novel-planning challenge with prizes galore.
#1474311 by Brandiwyn🎶

You have until the 3rd to sign up, but why wait?

And some fun ongoing things that don't require you to get into an October mood:

FORUM

Question of the Day!

(18+)
Come answer a question, share a laugh, encourage one another, and bring me a coffee!
#2142667 by Lilith of House Martell

No competition, no signup, just hop in and participate.

BOOK

Smile! (Groan?) You Know You Love These!

(ASR)
Want to smile at least once a day? Then read these! Okay, maybe you'll groan some too...
#2177903 by Sum1

What, I'm not funny enough for you? Add that blog to your favorites for a daily assault on your humerus.

There's plenty more going on here, of course, and I'm not trying to snub anyone by not plugging them right now. Feel free to add your own (or someone else's) in the comments below.

Tomorrow, it's back to the usual programming around here.

7 Like • Comment • View 1 comment

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