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Wednesday, Nov. 13, 2024

12:54am EST

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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:

Brandiwyn🎶

about 14 hours ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 4, 2024 at 10:43am

#1076238

Isn't It Draconic?

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~doingNaNo'24

Prompt 4. Sept 4.

Photo prompts. (Choose 1,2,3 or 4 and write fiction or non-fiction)

PhotoPrompt 3

Photo Prompt 3

I'm only posting the prompt pic I picked. One of the others was a blue rubber duck, and I almost picked that one, but dismissed it as "too cute."

Ducks and dragons are related, though.

A drake is a male duck. A drake is also, depending on the source, a particular subtype of dragon, or a synonym for dragon. The latter has a different etymology, one which is more apparent when you consider the adjective form, "draconic."

That should not be confused with "draconian," which is used to describe oppressive policies. Nor should it be confused with the explorer Sir Francis Drake, or his namesake Frank Drake, originator of the Drake Equation, which has nothing to do with dragons. Unless aliens are dragons. Which isn't technically impossible.

Another synonym for dragon is worm, or wyrm, which also confused me as a kid. English is weird.

Dragons are, unlike ducks, creatures of fantasy. Unless you count Komodo dragons, though I say that's cheating. But I have this hypothesis that dragons were dinosaurs.

Why were dragons part of the folklore of several geographically separate cultures? I think it's because of dinosaur bones. Some ancient t-rex or brontosaurus skeleton or whatever got exposed via erosion. Early humans, clever and creative but without our understanding of geological time, might have seen these enormous bones poking out of some sedimentary rock, and pictured what sort of creature might have made them. Clearly, it was a giant, flying, fire-breathing, gold-hoarding monster, because what else could it be?

But also, ducks are dinosaurs.

All birds are. Lots of dinosaur lineages indeed went extinct, but at least one survived into modern times and their genetically-plastic descendants exploded into the vast diversity of avian species we encounter today. Those eggs you had for breakfast? Dinosaur eggs. That KFC bucket you reluctantly bought over the Labor Day weekend? Kentucky-fried dinosaur parts.

Don't feel bad about eating chicken. Their ancestors probably munched on ours. Colonel Sanders was just doling out payback.

So, if you're wondering what a dragon would taste like... well, it would probably taste like chicken.

Or duck.

Unlike our modern birds, though, dragon meat might even come pre-cooked. All that fire breath had to do something to their insides, right?

Let's do this again. We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

5 Like • Comment • View 7 comments

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