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Monday, Nov. 18, 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:

tj-turkey-jobble-jobble-hard-J

about 11 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

September 30, 2024 at 3:01am

#1077469

Owl Miss This Place

For my final full day in Dijon, I didn't have anything planned out—no wine tours, no mustard discoveries, not even a "let's meet for lunch" (because unlike Paris and, by lucky chance, Tours, I don't know anyone here). So, as the day was fine and sunny and neither hot nor cold, I took a walk.

Dijon, like most European cities, is really quite incredibly old (from a US perspective). And, as with other cities, there's only so much one can do in a day. Turns out that Dijon has a self-guided walking tour embedded into it. Literally; there are brass plaques with engraved owls

on the sidewalks, pointing the way.

Why an owl? Well, on the side of the cathedral here (also named Notre Dame, because Catholics weren't very original) perches a small stone owl, barely recognizable as such from the accumulated wear of people touching it. Supposedly, touching it (but only with one's left hand) will grant a wish. Apparently, no one has yet wished for "restore the Notre Dame owl to its original carved glory." Or maybe they have, and it's just another silly superstition.

Following the trail eventually gets you to the owl, and then it moseys on along through other historic sites. It's like following the quest markers in a video game, which made me want to play a video game, but that can wait until I get home again.

I didn't touch the owl. For one thing, it's a silly (if mostly harmless to everything but the owl itself) superstition. For another, even if there were something to it, making a wish is tantamount to acknowledging that there's something missing in my life, and there isn't. For yet another, over half a century of reading and writing stories, and playing fantasy role-playing games, has instilled in me a deep, abiding distrust of wishes. And, for a final thing, some beggars were approaching with their cups out, so I hoofed it out of there, continuing to follow the brass owl arrows.

These led me next to a mustard shop, on the same street (Rue de la Chouette, naturally), where I finally got to see the thing Dijon is most famous for and holy condiments, Batman, there's a lot of mustard there.

At some point, though, around the Ducal Palace, I lost the trail and never did pick it up again, despite looking and even trying the internet. All I could discover was that it was not, in fact, the end of the trail. Oh, well.

Much later, in the evening, I returned to the palace area (Palais des Ducs) and its accompanying semicircular courtyard, Place de la Libération, which is surrounded by cafés, bistrots, restaurants, bars, and brasseries, the differences between which are subtle and very French. (Brasserie also means "brewery," but not all brasseries are actually breweries, much to my disappointment.)

Point is, I went back there for dinner because it's pretty, and I sat outside with a beer and a burger as the sun set and the Palais des Ducs lit up, and the shifting, multicolored lights in the Place's fountains illuminated their waters.

This sort of thing is one of the reasons I wanted to go to France.

9 Like • Comment • View 2 comments

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