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Thursday, May. 9, 2024

9:14am 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:

Lazy Writer est 4/24/2008

about 18 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 22 hours ago
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

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

February 22, 2024 at 8:54am

#1064670

Curiosity

Speaking of extraterrestrials...

Star Trek Starfleet insignia spotted on Mars

In case you were wondering what it would take for me to go through the process of incorporating an image into a blog entry (might have to scroll down), well, wonder no more. It helps when it's in the public domain. Less work. (credit: NASA/JPL-Caltech)

Like the infamous Face on Mars,

it's entirely possible that this particular example of pareidolia would go away, or at least diminish, under different lighting conditions or at a different angle or whatever.

Until then, let us Star Trek fans have our hour of glory.

From the linked "article:"

Amateur astronomer Scott Atkinson found the stone sculpture of the Starfleet insignia among a pile of rocks on the Red Planet's Mount Sharp (Aeolis Mons).

Just to be clear, Atkinson didn't travel to Mars or use a giant telescope; he apparently combed through the publicly available images from NASA's Curiosity robot. Well, they call it a rover, but come on; Mars is the only planet known to be inhabited solely by robots (to the best of our knowledge).

Curiosity itself (the robot) is a remarkable achievement. You can see more about it, and its images, here.

As of this entry, according to that site, the gadget has produced 1,165,040 images over 4105 sols, an average (because I can use a calculator) of over 280 photos/sol. Which would be a remarkable output even for a social media influenza.

Oh yeah, if you don't know, a sol is what they call a solar day on Mars. It's not too different from our own solar day: roughly 24 hours and 40 minutes.

More, all of those photos are transmitted, pixel by pixel, back to Earth. Truly a monumental achievement that this has been going on for, if I've done the math right, about 11 and a half Earth years, or roughly 6 Martian years.

Which is itself about four times as long as the original Star Trek series aired.

I wrote yesterday about the possibility of encountering alien life. But if we ever encounter technologically capable aliens, given our own history of exploring with robot probes before sending humans out there, it wouldn't surprise me in the least if our first contact was with one of their machines.

Those machines might send back videos of Star Trek, and since a sense of humor appears to be a requirement for technologically advanced life, they'll probably freak us out by showing up dressed as Ferengi.

And here I was planning on talking about how the image clearly shows indications of erosion, which is cool enough by itself without invoking science fiction. Oh, well. Sometimes I go in unexpected directions, which proves I'm not an alien robot.

Or does it?

3 Like • Comment • View 2 comments

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