Complex Numbers (Book)

Blog Calendar

◄ February ► 2023
S	M	T	W	T	F	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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🎶

a day 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

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!

4 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.