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Wednesday, Sep. 11, 2024

10:15pm EDT

Members: 940

Guests: 1,081

Total Online: 2,021

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:

Aiva Raine

about 7 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

Wordsmitty ✍️

about 9 hours ago
In response to "Drop and Gimme Twenty"

Wow. That sounds mature for twenty. Next year you can get some booze to celebrate.

I'm sure we're all glad you did sign up. Enjoy the day.

1 Like

Annette aka Din Djarin

about 9 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th to you!

My username was octobersun2 for the same reason. My first attempt to join somehow didn't work.

1 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Drop and Gimme Twenty"

Happy Anniversary, you old dog...

1 Like

Kåre Enga in Montana

Sep 9, 2024 at 10:57am
In response to "Time Out"

"As long as everyone agrees to it" is paramount.

The Polynesians navigated by the stars. No clocks needed. A different approach. Still... all relative.

1 Like

Legerdemain

Sep 9, 2024 at 10:47am
In response to "Time Out"

I'm not scientific, at all. But what about Earth's wobble? Who accounts for that?

1 Like

🌕 HuntersMoon

Sep 9, 2024 at 10:20am
In response to "Time Out"

This was so heavy... I think I lost 26 microseconds reading it.

1 Like

Elisa: Middle Aged Stik

Sep 8, 2024 at 12:04pm
In response to "Writing It Off"

I am late to the party with my comments, but here we go.

Used to be, I wanted to get published.

I used to want to be published in terms of stories. Nowadays I'd rather be published in terms of photos. And self publishing may be my only option in that regard.

but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

And before that it was crowded with middle aged socialites with nothing better to do (but did have some level of writing skill).

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay.

I admit that as of late I don't let my book items hit the entry limit. Part of it is my entries are super long (current average being *checks notes* 7.48 kb in size). Part of it is I also feel like book items should end after at most five years. I think of my old paper diaries and how they felt more meaningful when I didn't let their use drag on forever. If I stayed consistent, they'd end maybe at most after a year and a half. They often wrapped up sooner than that. Even moving to online journaling, I appreciate a journal that is finite not based on the number of entries but by time elapsed since the book started having entries added to it. My current journal may last a tad longer than my previous ones, but I imagine I'll wrap it up in late 2027, maybe early 2028. We'll see how much space I have to work with. In the old days, 1000 entries was considered a major achievement of an end point. I hope I can get that much out of it, as I think that's more reasonable. I do think 3000 entries of my kind of work in one place is a bit much.

1 Like

🌕 HuntersMoon

Sep 8, 2024 at 11:00am
In response to "Revisited: "Orange You Glad This Wasn't You?""

Maybe this would help... or at least attract your attention?

1 Like

Robert Waltz

Sep 7, 2024 at 11:39pm
In response to "Spit in the Ocean"

Both commenters today had already received MBs from me this week, so I went back to every entry this week and picked a comment at random.

The final Birthday Week MB goes to:

🌕 HuntersMoon

Thanks, everyone, for reading and participating!

1 Like

August 18, 2024 at 10:39am

#1075432

Revisited: "Challenge Complete"

Today's cruise on the river of time takes us back to the end of January, 2019. This was a 30 Day Blogging Challenge month, and for context, my current daily blogging streak wouldn't start for another ten and a half months. And, of course, it was before everyone's lives got disrupted.

The entry itself, "Challenge Complete"

, featured the kind of prompt I came to expect for the final entry into that challenge:

Write a list of at least 5 blogging prompts to add to the Challenge War Chest to be used for future rounds of the 30DBC. Then, use one of your own prompts to write your entry.

I've never really enjoyed coming up with prompts. Scratch that; I do enjoy it; it's just that when I'm expected to create one, my mind goes blank. I know this sounds odd from someone who's been judging "The Writer's Cramp"

[13+] and therefore coming up with a prompt almost every week for nearly two decades, but there you have it. I just think of it as another challenge for myself.

The actual prompt list I came up with is uninspiring to me even now, and I won't quote it here. It's there at the link if you want. I'll just address some of the other things I said in the entry.

I don't know who coined the term "bucket list," and I can't be arsed to find out.

Unlike most words and phrases, they've traced that phrase in its "things to do before you die" sense to a precise moment.

I do know that it became the title of a moderately interesting movie with Jack Nicholson and God.

According to that link I just did, the phrase's origin and the movie title came from the same place.

While I've been known to use the phrase from time to time, I usually call it my "fuck-it list." This is because I've already done most of what I set out to do, and have given up on the rest.

Good to see my attitude hasn't changed in five and a half years.

It's come to my attention recently that life is much less frustrating if you can separate "things that I cannot control" from "things that I can control," and to focus on the latter while letting go of the former. This is something akin to the infamous Serenity Prayer, which I resent because a) it's a prayer and b) it's associated with AA, and AA is for quitters.

That's not my actual problem with AA, but it made a decent joke.

I've been walking every day for the past 5 weeks, which is, like, a new record for me for exercise.

I should have kept track of my record for "days without formal exercise." It'd be a lot longer.

Say I want to take a trip to space. How can I make that happen? Well, probably by paying Virgin Galactic a very large sum of money to fire me into a suborbital trajectory that technically takes me 100km up for a fraction of a minute, thus putting me, by definition, in space.

I think that particular venture never took off (pun intended). Branson lofted himself into a suborbital trajectory, but his maximum altitude was somewhat less than the accepted boundary of "space." Pretty sure I wrote about it in here at the time. Then Virgin declared bankruptcy. Or something. I can't keep up with all the rocketing these days.

Honestly, even if I were a billionaire, this would strike me as a colossal waste of money.

While I accept that other people wouldn't find it so, paying any amount of money for fame and bragging rights.

So here's the real example: I want to be published.

Yeah, not so much anymore.

Not much else of note. Kind of a boring entry, even now. Only one joke that I could find, and it wasn't even original.

Can't be "on" all the time, I suppose, but some challenges are never complete until the day you kick the bucket.

1 Like • Comment

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