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Sunday, Nov. 10, 2024

3:29pm 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:

Kåre เลียม Enga

a day ago
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

a day ago
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

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

September 7, 2024 at 7:20am

#1076413

Spit in the Ocean

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~doingNaNo'24

Prompt 7. Sept 7.

The world is not an ideal place for lots of people. What can YOU do to make it better?

Well, the one most overwhelmingly important thing I have already done is: avoid bringing another human into a far-from-ideal world.

The second most important thing is that I attempt to bring knowledge and comedy into an ignorant and largely humorless world. In that, I fail most of the time, but at least it makes me feel good to try.

And there are other things I do. I recycle, to the extent that I'm able. I help out with causes, when I can be sure that it's going more to the cause than to the organizer. I try to minimize my water use, and refrain from littering. All of that amounts to spit in the ocean, and it doesn't even make me feel good to brag about it. And for every infinitesimal improvement we can make individually, millions of times worse stuff gets done by other people, governments, and big corporations. "Every little bit helps," my ass. You think it makes a difference if you give a dollar to a billionaire? No, they only notice if you try to take one.

If there's anything that the pandemic years drove home to me, it's that any effort we make has to be a collective effort—and that it will never be a collective effort. There will always be those who deliberately make things worse. If an asteroid were about to hit the ocean, and the only way to avoid it would be for everyone to, I don't know, jump up and down at the same time, at least half the population will continue to sit on their asses, out of ignorance, apathy, a death wish, or maybe just plain spite. "The other political side wants me to do this, so I absolutely refuse to do it."

So you're jumping up and down... for what? Some marginal improvement in your fitness? So you can say you're at least trying to help? I mean, in that particular case, I'd probably do it, just on the off-chance that everyone else will, too. But they won't.

Yeah, some people are in a position to make improvements now, and I wish them the best. But I'm not in that position. What we need are big, systemic changes, not that one extra dollar.

I can travel less, reducing my carbon footprint.

I can move to a plant-based diet, helping the environment while reducing animal suffering.

I can drive less, walk more. (I know this because I spent over a year without a car.)

I can volunteer my time to causes I care about.

I can mentor youth, sharing my vast intelligence and infinite wisdom with the impressionable younger generation.

Yes, I can do all these things.

But I won't.

FINAL DAY! 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.

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