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Friday, Apr. 11, 2025

3:10am 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:

tj wanderlust-words-in-motion

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

tj wanderlust-words-in-motion

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

Soldier_Mike

Mar 10, 2025 at 11:46pm
In response to "Revisited: "In Spite Of""

Tangentially related to 6. Adidas and Puma: During my first tour in Germany, I was assigned to the Army agency that formerly occupied Herzo Base, an airfield probably located within medium mortar range from the sport shoe factories.

As far as German revenge is concerned, I would venture a guess that it's planned down to the smallest detail and executed with appropriate gusto.

tj wanderlust-words-in-motion

Mar 10, 2025 at 6:31pm
In response to "Automatic for the People"

Earlier today I did a bit of shopping. I found a couple of items I had not planned on purchasing on sale so I grabbed them. As the cashier rang them up, I noticed they did not register the sale price, the regular price, but an even higher price. I questioned it and was told this, "The sale ended yesterday, but we didn't get the sign changed. Today the price increased because our cost has now increased." Yes, how did you guess, one of the items was eggs, now over a dollar each!

1 Like

February 7, 2023 at 12:01am

#1044382

Pareidolia

Another entry for "Journalistic Intentions"

[18+]. This one can be found here: Faces Everywhere

Pareidolia

is popularly known as the tendency to see a face or figure in accidental places. Examples include the Man in the Moon, the Face on Mars (it's not a face), and the ever-popular Jesus toast.

Or, speaking of Jesus, some people find him in a dog butt.

I'm not judging. But it does confound the proverbial dyslexic agnostic insomniac, who stays up all night wondering if there's a dog.

In the case of today's prompt image, though... I'm not seeing it. Looks more like a grasping hand to me. Which is a form of pareidolia, but the title of the image led me to expect to see faces. Generally if I go into something with that expectation, I'll see it. Not this time.

This could be related to my partial face-blindness. A while back, I tried to get back into my bookface account so that I could delete it. I'd forgotten the password, so they issued me a challenge: identify the people in these photographs, ripped from my friends list.

Leaving aside the ones who I only knew from online, whose faces I wouldn't recognize anyway, I haven't seen some of my failbook friends in decades. And even absent those, I'm just not that great at identifying faces. Hell, one time I was at a bar doing a trivia contest. I had barely even started drinking yet, and the goal was to identify the famous people in a set of photos. I recognized a couple of them, but one that I didn't was... Bruce Springsteen, circa 1985. You'd think if I could recognize anyone, it's him. But no.

Long story short, this is why I still have a facebuck account: I can't get back in to delete it. And it's also why I don't always see pareidolia.

One thing that occurred to me a while back, though, is that artists rely on pareidolia. That is, I don't mean the examples in the Wiki link above, but, like, cartoon artists. They can throw together a few lines, and it looks like a general face (even to me). That's deliberate, though, and doesn't involve chance formations in nature.

Now, I could go into speculation about why we see faces everywhere, like the late lamented Old Man of the Mountain in New Hampshire, and make some guesses about how it was advantageous for our ancestors to think they saw faces. But I won't, because that's all it would be: speculation. The facts we know include that we do see faces or figures in natural objects. And sometimes that's fun.

But sometimes, it leads to wild conspiracy "theories," like with the Mars thing. Some alien must have carved it! Well, no, it's just pareidolia.

Which doesn't explain why there's a smiley face on Mars

. Do you see it there? That's the crater Galle in the Argyre Planitia. Might be easier to parse in this photo.

Okay, yes, it totally does explain it. Completely coincidental. Just because Mars is the only known planet to be inhabited solely by robots doesn't mean that said robots did that for our benefit.

Have a nice day!

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