The Mathematics of Beauty

I'm in the same boat. I call it a quanswer.......ie each answerable level poses a likewise complexity which is definable only by having asked the question.....

sunshine comes to mind

How we define Beauty? It depends on the state of mind. It changes from time to time , place to place, culture to culture. Beauty depends on the human physicalogy. Beuty is universal but definition varies not like mathemetics. we donot know how the animals ,plants, insects feel regarding beauty. Mathemetics is universally accepted as 2x2=4 but i feel may be upto some extent beauty related with maths but not fully. Maths is unick but Beauty cant be defined 100%. This is how I feel. Whatyou say?

okp Sarma

If plastic surgeons use Nefertiti as an example of beauty how come they end up with so many "Ski Jump" noses ?

I suppose it a bit like a garage mechanic moaning -

"You just can't get the parts these days"

Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were influenced by mathematics and was an inspirational source for Plato and Platonism. Plato introduced his famous triad of Truth, Goodness, and Beauty as the fundamental argument for the existence of gods and man. This Triad has been adopted by the "intelligent design" group in their defense against evolution. So, philosophy, mathematics and now religion has been rooted to the simplicity of how mathematics has influenced our understanding of truth, goodness and beauty in the western world.

In the eastern world, Confucius and Buddha taught the philosophy of the "Golden Mean", yes, which traces moderation in all things, as described by the "mathematical mean", and which brings harmony to life. So chew on this bit of philosophy, religion, and mathematics—while hunting for the hadrons and god particles in the LHC at Cern.

I was sure that "beautiful" face looked familiar:-

Wow! Hmmm. Well first off. I would agree that there is mathematical meaning in everything in nature as well as man made things. I would disagree in the concept of what "beauty" is. After all throughout time it has been proven that beauty is in the eye of the beholder. That diagram, which may be absorbing to some, may be utterly distasteful to others. Mathematical or not, this theory has many flaws. I suppose mathematical beauty and artistic beauty will clash here. I do believe the the absolute that mathematics offers. Does it make for a perfect beautiful face? I theorize not. The love of art in me though appreciates the rare beauty that subtle variations in features give. If everyone looked like the above concept, it would be a cloned world. That facial shape doesn't really give for many other races either. What makes a race a race is their distinct differences that set them apart from other races.. hence, the shining of many different beauties and features. Just throwing that out there..

Sarah

Last I heard truth was beauty.

Just kidding...

As far as mathematical conformance of images or sculpture, or any of the visual arts and sciences I feel compelled, and work to achieve conformance to those rules.

In many other areas I may be considered rebellious, though one of my friends once said I was so sane, most people mistook it.

At anyrate, in this case I am a very strong believer in the Golden Mean, and what I work with when making images on paper, canvas or wood, is the Rule of Thirds, and balance.

It was late in my art career that anyone proffered mathematical reasons for what I liked.

So I came to the math of it more as a confirmation out of another field than making attempts to make the art conform to any math.

A good friend of mine made a wood stove according to precepts of the Golden Mean, and I tell you it is one very efficient woodstove.

Facts of beauty do challenge realities.

For instance beautiful women typically have a flaw in the perfection, as even Angelina Jolie has big lips, and Marilyn Monroe, a mole.

Some artists overpower us with content. :For instance Hieronymus Bosch or Salvador Dali nearly call that you, by your own eye and framing see their paintings in series of frames on one canvas.

Always in the visual arts there is some conflict between content, and composition.

That which is memorable must be flawed, or it is too beautiful to register.

Well put.

Visual impact is just that...warts and all. The rule of thirds is a convention rather than some mathematical vectoring principle. Assigning vectors and geometric beauty is more an exercise in structure...albeit a valid one to some degree.... it still does not accomodate the principal of emotion that colour and form induce.

Personally I find realism quaintly boring. It's structure depends on detail and is intended for audiences unaquainted with out of the tube thinking. Futurists and Fauvists were interesting but lost their way. Dada, on the other hand will never die.

JFK once said that art is a form of truth. His perspicacity surprised many.

"Peitgen and Richter, The Beauty of Fractals"

One of my favorite tools for exploring fractals is XaoS. A particularly nice feature of XaoS is its ability to render animations together with a built-in scripting language that lets you vary just about any parameter you wish during the animation and for other compositions.

Here are some stills I've made using XaoS ...

#1 - Also from the Black Lagoon

#2 - American Southwest

#3 - Bold

#4 - Ribbons 'n' Bows

#5 - A Midsummer Night's Dream

#6 - Dragon's Eye

#7 - Foiled Again

#8 - Christmas Bows

#9 - Throne Room

#10 - Silken Sun

#11 - DVD

#12 - Fiddlehead

#13 - CyberPriest

#14 - Dora The Explorer, Acid Queen

#15 - Heaux, Heaux, Heaux

#16 - Dome Alone

#17 - Intake

#18 - Pebbles

#19 - Soft as Ice

#20 - First Frost

#21 - Snowflakes

#22 - Pleats

#23 - Pan-Dimensional Coat Hook

#24 - The Ghost In The Machine

#25 - Jade Necklace

#26 - The Big Sneeze

#27 - String Theory

#28 - There Goes The Neighborhood

#29 - Quarry

#30 - Where is Area 51? I'm late!

#31 - LaceWing

#32 - Trilobite

#33 - Tinfoil Hat

#34 - Silk I

#35 - Silk II

#36 - Starfish

#37 - Shield

#38 - Lace

#39 - Untitled

#40 - Tinfoil Hat Redux

#41 - Neutron Star

#42 - Untitled

Enjoy!

-e

Thank you kindly--these are beautiful!

I don't recall seeing any Maurits C. Escher in this thread, but there is another great combiner of mathematics and art.

I'm not much of an artist, but to me, most of those qualify as 'beautiful'!

Dick

You should make this stuff it's own thread. I think a lot of people would be interesting (including myself).

I hate to say it, but don't you mean 'interested' ? _{<walks away and slaps self for cheap gag>}

I think he meant say "interesting." I don't know about you and Roger, but that's why I drink.

I admit it, I find myself a lot more interesting after a few drinks.

Good for you, Roger. Ignore Duck and e-man. Folk always say I'm "curious". I just love a compliment.

I just love a compliment.

I don't care what anybody says. I think you're marvelous!

I did mean interested, but I like how it came out and I'm gonna stick with interesting.

Most sporting of you.........that'll qualify us for our 15 megabytes of fame............

What's a megabyte?

Lipservice

You should make this stuff it's own thread.

I agree: the names europium has chosen are great. But, perhaps a good way of generating lots of posts would be to "publish" them without, and, ask people to come up with their own names.

Am I the only person who's going to give him a GA?

"...ask people to come up with their own names."

An awesome idea! How's about I start a new thread "Name That Fractal" and list them by reference number only. Then, others can post their own names with the reference numbers. Would that work?

I'll name the first two Fib & Archie

OK, tricky: I suppose you could add a thumbnail to each pic. and ask people to copy and paste the thumbnail with the suggested name:-

39

39 From here to eternity.

Or just post one a week Like the caption this competition

www..........Weird.Wild.Web

Recurse you, Randall! That link links to Post #142 ...

Back in like 1986 I was putting on light shows with projectors and film at a club called Club Zero. This was in Rochester, NY.

There was a competing club nearby in town that got a video feed from somewhere that utilized imagery very similar to what Europorium has put up.

The images of course moved from one to another and were presented on video screens.

I am sorry I cannot provide where that feed came from.

There is a real argument about the subjectivity of beauty within the human species, but, as the only species which seems to appreciate beauty, you can present something like a rose to any culture and, except for abhorrent individuals, will find it beautiful. There does seem to be something universal about beauty within the human perception. And, of course, Roses follow Phi in their growth pattern.

When one considers that there are an infinite number of series which could be defined it's hardly surprising that someone will find one which correlates to some naturally occurring phenomenon.
Del

There is nothing ugly in art except that which is without character (August Rodin)

I am come to The Law of The Flaw, as an explanation of conflicting sources of perfection of Art in a frame.

Movement and meaning, Content and Composition are to be turned by the hand of the artist into Beauty.

At one point in the work there is a leap that mathematics can only seek to explain, and cannot predict.

The flawed face in the picture is beautiful, whereas the flawed numbers insure the bridge will fall over in the wind. The ugly ponderous bridge is loved and beautiful for not falling down.

There may be someone who was killed when a painting fell on them, but I haven't heard of it, and would expect it to be more a disaster of some really heavy sort of frame.

What Bridges are Beautiful, and Will Last forever?

What Paintings have lived longer than ponderous, or beautiful bridges?

Thanks for posting the great fractals. (I love playing with fractal trace software in the gimp.)

Here's another mathematical beauty and a work of engineering to boot: found art, author unknown. The math involved in producing this in a wireless signal is a bit beyond me. It would be better reproduced as a video, (and the 'birds' made to flap their wings I say!). But here's a short snip.

That is an example of a moiré pattern.

There's moire to that than meets the eye, although in terms of art it will always be on the fringes. _<groan>
Del

You should be punished. Put in a punitentiary, even.

Besides, moiré is pronounced moi-yay, moi-fo.

Go figure. Interesting read. I encountered the moire effect before, one time when I was trying to take pictures of cloth, but didn't know what it was called (other than damn nuisance).

I see it has some uses (none of them, however, art!)

Don't tell that to this guy!

I guess I slipped off topic - there's way more to art than beauty alone, and nothing is excluded from art (for long!)... Pip's moire pieces convey a sensory richness of colour and texture, but not so much in the way of beautiful form. (I think they are intended to play upon peripheral senses, more so than to be a focal point. ?maybe )

I think the most beautiful things, the ones that hold my attention, even if they are mathematically planned or generated, always have an irregular quality that conveys the degree of uniqueness that a natural object or living thing has. Maybe there's more to it than that....

But I'm partial to irregular things, so it could be just personal taste.

Would you adam 'n' eve it; I was catching up on the papers and found this.

_{wonder if there's mush room for this kind of example}

My fave by Daniel White and Paul Nylander is Hell Just Froze Over...

...from the inside of the Mandelbulb you posted above.

Daniel eats anything made of Quorn I have a nephew who was born there ! Cool pics in that second link

Brooklyn Museum Announces New Egyptian Installation: "The Mummy Chamber"

Click on the coffin, the mummy and the objects to learn more about them. Ancient Egyptian time Ancient Egyptian life There were six main parts to ancient Egyptian temples built during the New Kingdom period. These parts are: • The pylon • The courtyard • The hypostyle hall • The second hall • The sanctuary • The sacred lake Explore the temple to find out why each of these parts was important and why temples were built the way they were.

Temple of Luxor, Egypt

The Egyptian Pyramids

The Egyptian Pyramids Engineering

Outside the pyramid The Great Pyramid was part of a complex that included a special walkway, two temples, other pyramids, boat pits and the mastabas of nobles. Read a Story about the building of Great Pyramids.

Trades of Ancient Egyptians

The Ancient Egyptians Pharaohs

See beautiful photos of Egypt: http://www.ancient-egypt-online.com/queens-of-egypt.html

since this golden ratio excist in every thing humans, plants, this means that the founder , the creater is one and only one "ALLAH", you can go to the google earth and look for that gplden ratio for the position of MECCA. and let me know.

salam

The Golden Ratio is intrinsic to a Pentagon. Somewhat satanic. In the context of religion, people will have to just go figure.

Pure Phiction.

Don't you mean phallacy ? Spelling never was my strong point.

Don't you mean phallahcy?

"Spelling never was my strong point."

I can't say if it never was (as I wasn't there for most of it), but it sure isn't now!

Ha! My spelling sucks and so I depend pretty heavily on spell-checkers to make me look cosmetically literate.

I wouldn't get my pantiesknickers in wad over it, though; not if I were you. What your spell-checker lacks in lexical skills is more than compensated by your most excellent punmanship.

punmanship..
Is that a pismelling of punishment?

I tell ya, I've been on bended kness with Mark (mgauilin), asking for a 'Gramaticatator'. I'll just have to keep sucking up to Admin. Hard work, but the donut crumbs kind of compemsate. Shame about the LHC, but I think that was bagels.