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Wednesday, Nov. 13, 2024

1:44am 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 15 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 3, 2024 at 10:05am

#1076171

To Love Until I Laugh

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~doingNaNo'24

Prompt 3. Sept 3.

You can achieve all the things you want to do, but it's much better to do it with loved ones around you; family and friends, people that you care about that can help you on the way and can celebrate you, and you can enjoy the journey. ~John Lasseter

Your most significant other(s) is/are....! Write about your loved ones (furry or not).

Right, as if I were capable of love.

Okay, okay, that's a joke, and I'm determined not to make today's entry as existentially terrifying as yesterday's. But as I showed then, you can't count on anyone. Just saying. And not just because I was given up for adoption as an infant, either.

Still, "love" carries a lot of baggage and assumptions. The Greeks might have gotten it closer to right by slicing it up into sub-loves: eros, agape, whatever. They say the Inuit have dozens of words for snow. While this is probably false, like all legends, it illuminates what might be a greater truth: the more important a concept is culturally, the more words they'll have to describe its various shades and gradations. We just have two words for love: love itself, and like.

We've got dozens of words for killing, though. And hundreds of words for penis.

All of which is to say that while there are people (and cats) that I particularly care about, I neither have nor want a "significant other." I've been married twice, and you know what Einstein supposedly said about the definition of insanity.

Einstein probably didn't say that, though, and it's not really the definition of insanity.

You know who (probably) did originate that quote, though? According to some of my fact-checking sources, in its current form ("Insanity is doing the same thing over and over again and expecting different results"), it was Rita Mae Brown, in the voice of one of her characters.

Rita lives near me. I met her a few times. Exceptionally nice lady. Cat person. I suspect she found it extraordinarily amusing that her quote became misattributed to the guy whose picture is in the dictionary under "genius."

Well, enough with the name-dropping. If it helps, I live near John Grisham, too, and never met him.

The point is, these days, I'm done with that sort of love. You know how some guys, they'll meet someone of their preferred gender, and their mind immediately fast-forwards ahead to the sex part? Mine fast-forwards to the breakup part, and I don't want to deal with that again.

But I have friends. And cats. That's enough for me.

Because if there's one thing I learned early and took with me into adulthood, it was how to be comfortable being alone. It always surprises me how much other people depend on each other, as if that rug won't be pulled out from under them at some point. Some say the pain of eventual abandonment is worth the pleasure of another's company, but I'm not so sure.

Don't dare think I'm bitter about it, though. I get that some people would be, but I'm not them. Mostly, as always, I'm amused, and laughter is one constant friend I can count on.

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.

2 Like • Comment • View 3 comments

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