Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ January ►
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	29	30	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Monday, May. 20, 2024

5:08am EDT

Members: 697

Guests: 990

Total Online: 1,687

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

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

January 11, 2024 at 11:06am

#1062201

Seeing is Disbelieving

The Random Number Gods have chosen to bless us with another Cracked article this day.

4 Illusions That Trick You in Your Everyday Life

And no, one of them isn't "time." Well, the last one is. Sort of. Not really.

Don’t believe your eyes. They lie to you every day.

I might have mentioned this before, but I used to work with a guy who was constantly showing me optical illusions. As he was an engineer with more experience than I had, I thought he was trying to train me to believe the measurements and numbers more than my visual perception. But no; he was also a devout Christian and was trying to show me that only God is real or whatever.

Thing about those optical illusions you can find all over the internet is that most of them have documented, logical, proven explanations. So all that did was reinforce my admiration for science.

4. Your Nose Is Smaller Than Selfies Tell You It Is

Long ago, I was a semi-professional photographer (in that I got paid for it, but it wasn't my main source of income). This section reiterates what I've known for a long time about the difference between focal lengths.

For authentic pics, never hold your phone up close. Instead, set up a tripod several feet away, inconveniencing everyone in the name of better art.

Like anyone's gonna do that. Just hand your phone to some random stranger and ask them to take the pic. There's a very good chance you'll even get your phone back, afterwards.

3. The Moon Keeps Changing Its Size on You

Yes, this one was the real reason I saved this article to share.

If you’re lucky enough to see the Moon rise or set over the horizon, you’ll notice it looks different from how it looks when it’s high in the sky. It looks a bit more yellow, due to the greater amount of atmosphere that moonlight must travel through to reach your eyes from this angle. It may also look slightly squashed, which is another effect of looking at it through so much atmosphere.

I should note that there are times when the Moon really is bigger or smaller because its orbit, like pretty much every orbit, is elliptical. This horizon illusion dwarfs that effect, though, at least in my experience.

More than anything else, however, the low Moon simply looks much bigger than the Moon as you normally know it. Everyone sees this difference, and no one knows why.

Perhaps, but I'm convinced it's a combination of things. Including a version of the Ponzo Illusion

(not to be confused with the Ponzi Scheme). Flat Earth (not really, but we perceive it as such), mostly flat sky converging on it. Also the convergence of the two horizon lines. I'm sticking with that hypothesis until smarter people than me figure something else out. That might take a while.

2. They’re Using Color to Lie About Produce

Ever since that photo known as The Dress exploded into public consciousness, I've seen more and more articles explaining color perception. I got really tired of seeing it when it first happened, but apparently, some good has come from it in terms of public perception of color perception.

1. Clocks Look Like They Stop Because They Break Your Brain

Despite what I said above, no, time is not an illusion (probably). As with color, though, our perception of time can change with circumstances.

The article goes into the science here, and since it tracks with stuff I already knew, it's absolutely worth reading. Spolier: it's not a glitch in the Matrix. There is no Matrix, except in the movies.

In conclusion, my mom always told me "seeing is believing." Sorry, Mom. You were wrong.

2 Like • Comment • View 2 comments

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

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/1-11-2024