fractals?
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RedGlitter
- Posts: 15777
- Joined: Thu Dec 22, 2005 3:51 am
fractals?
This may be stupid, but how do fractals work? I've looked it up online and it's always gobbledegook to me. I am poor at math and I understand it's a math thing but is there a way for a math dummy like me to understand how math becomes a design? 
fractals?
I don't have enough to explain it, but music is mathematical as well. Even fractually.
And if you listen to an old Lou Reed album called Metal Machine Music you may even find chaos theory!
And if you listen to an old Lou Reed album called Metal Machine Music you may even find chaos theory!
fractals?
How about this.
Look at your hand.
A hand.
Look at the skin of your hand.
Skin on your hand.
Look closer. You'll see cells of skin.
Cells of skin on your hand.
What you first saw as one you now see are made up of many.
It's infinite.
This hurts.
When I got into quadratic equations in college I had an anxiety attack.
Look at your hand.
A hand.
Look at the skin of your hand.
Skin on your hand.
Look closer. You'll see cells of skin.
Cells of skin on your hand.
What you first saw as one you now see are made up of many.
It's infinite.
This hurts.
When I got into quadratic equations in college I had an anxiety attack.
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RedGlitter
- Posts: 15777
- Joined: Thu Dec 22, 2005 3:51 am
fractals?
Quadra what??! I know of Quadrophenia the album. Jacksdad, my head is already blowing up. Oh wait- nope, I'm dead. :yh_ghost
Seriously, I've wondered for years how those fractal things are made and it stumps me. Music is mathematical...I think I learned that today is my "Music of the Spheres" thread but it's all so beyond me. I get the hand thing though so there's hope for me.
fractals?
RedGlitter;548213 wrote: Quadra what??! I know of Quadrophenia the album.
Jacksdad, my head is already blowing up. Oh wait- nope, I'm dead. :yh_ghost
Seriously, I've wondered for years how those fractal things are made and it stumps me. Music is mathematical...I think I learned that today is my "Music of the Spheres" thread but it's all so beyond me. I get the hand thing though so there's hope for me.
S'ok. I understand.
I like to keep a roll of duct tape nearby to wrap around my skull.
That way if it explodes the parts will be easier to find.
Nods to Glenn Beck.
Quadra what??! I know of Quadrophenia the album. Jacksdad, my head is already blowing up. Oh wait- nope, I'm dead. :yh_ghost
Seriously, I've wondered for years how those fractal things are made and it stumps me. Music is mathematical...I think I learned that today is my "Music of the Spheres" thread but it's all so beyond me. I get the hand thing though so there's hope for me.
S'ok. I understand.
I like to keep a roll of duct tape nearby to wrap around my skull.
That way if it explodes the parts will be easier to find.
Nods to Glenn Beck.
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Indian Princess
- Posts: 1953
- Joined: Fri Nov 03, 2006 4:55 pm
fractals?
Jacksdad- THANKS FOR THE LAUGH!!!!!!!!!!!!!!!!
I thought I was the duct tape queen, always in my car buddy, oil cap came off lost?
Dont ask how, so I whipped out my handy dandy duct tape slapped that on there drove it for a week, went to the junk yard and obtained a new one, however, the gentleman assisting me laughed so hard he gave it to me for free......
I thought I was the duct tape queen, always in my car buddy, oil cap came off lost?
Dont ask how, so I whipped out my handy dandy duct tape slapped that on there drove it for a week, went to the junk yard and obtained a new one, however, the gentleman assisting me laughed so hard he gave it to me for free......
fractals?
I'll try, but I'm not good at this sort of thing. Explaining. People end up confused.
There's a class of equations which take a calculated value and recycle it until a consequence emerges, and they can look generally like:next x = (a sum involving x) + (a constant)The consequence of running this round and round is that you can eventually tell whether you're tending toward a final fixed answer or you're diverging indefinitely with no hope of reaching a final fixed answer.
Take (a sum involving x) to be (x+1) and the constant to be zero, for example. Starting with (x=0) and running that round and round gives you a series of 1, 2, 3, 4, 5 etc and it's apparent that it isn't converging on a final answer.
Another example that diverges, take (a sum involving x) to be (x squared) and the constant to be zero. Starting with (x=2) and running that round and round gives you a series of 4, 16, 256, 65536 etc and it's apparent that's not converging on a final answer either.
So, without a numeric example because it's getting tricky, there are some initial equations and some starting values of x and the constant which will, unlike those, converge.
A fractal builds from an equation which is inherently unstable. One starting state will diverge, say, while a very similar starting state will converge. The classic equation which does this was the second of my earlier examplesnext x = (x squared) + (a constant)where x and the constant are complex numbers, the starting value is (0,0) and the constant is the coordinate on the plotted picture represented as a complex number. Leaving all the points black if they don't diverge, the Mandelbrot fractal pattern shows a different colour to represent how soon the equation proves to be divergent for a given constant in the starting state.
The prettiness of the pattern is that however closely you focus the plotted area on a boundary between divergence and convergence you don't get any less complicated a boundary. However tightly you magnify, you're still left with a similar degree of instability at the edge. The colouration is there in the picture just to make it look good, it only indicates how fast the equation resolved into a divergent state from the starting condition.
Until you hit a molecular scale, the real world looks the same. If you consider the UK coastline and measure it around the edge to the nearest kilometer you get a length. Change the accuracy of the measuring to a meter and you get a different length as you incorporate more twists and turns. Go down to a millimeter scale and the length of the coastline is longer still. The coastline, until you hit molecules and have no smaller units to measure, is fractal.
There's a class of equations which take a calculated value and recycle it until a consequence emerges, and they can look generally like:next x = (a sum involving x) + (a constant)The consequence of running this round and round is that you can eventually tell whether you're tending toward a final fixed answer or you're diverging indefinitely with no hope of reaching a final fixed answer.
Take (a sum involving x) to be (x+1) and the constant to be zero, for example. Starting with (x=0) and running that round and round gives you a series of 1, 2, 3, 4, 5 etc and it's apparent that it isn't converging on a final answer.
Another example that diverges, take (a sum involving x) to be (x squared) and the constant to be zero. Starting with (x=2) and running that round and round gives you a series of 4, 16, 256, 65536 etc and it's apparent that's not converging on a final answer either.
So, without a numeric example because it's getting tricky, there are some initial equations and some starting values of x and the constant which will, unlike those, converge.
A fractal builds from an equation which is inherently unstable. One starting state will diverge, say, while a very similar starting state will converge. The classic equation which does this was the second of my earlier examplesnext x = (x squared) + (a constant)where x and the constant are complex numbers, the starting value is (0,0) and the constant is the coordinate on the plotted picture represented as a complex number. Leaving all the points black if they don't diverge, the Mandelbrot fractal pattern shows a different colour to represent how soon the equation proves to be divergent for a given constant in the starting state.
The prettiness of the pattern is that however closely you focus the plotted area on a boundary between divergence and convergence you don't get any less complicated a boundary. However tightly you magnify, you're still left with a similar degree of instability at the edge. The colouration is there in the picture just to make it look good, it only indicates how fast the equation resolved into a divergent state from the starting condition.
Until you hit a molecular scale, the real world looks the same. If you consider the UK coastline and measure it around the edge to the nearest kilometer you get a length. Change the accuracy of the measuring to a meter and you get a different length as you incorporate more twists and turns. Go down to a millimeter scale and the length of the coastline is longer still. The coastline, until you hit molecules and have no smaller units to measure, is fractal.
Nullius in verba ... ☎||||||||||| ... To Fate I sue, of other means bereft, the only refuge for the wretched left. ... Hold no regard for unsupported opinion.
When flower power came along I stood for Human Rights, marched around for peace and freedom, had some nooky every night - we took it serious. [Fred Wedlock, "The Folker"]
Who has a spare two minutes to play in this month's FG Trivia game! ... My other OS is Slackware.
When flower power came along I stood for Human Rights, marched around for peace and freedom, had some nooky every night - we took it serious. [Fred Wedlock, "The Folker"]
Who has a spare two minutes to play in this month's FG Trivia game! ... My other OS is Slackware.
fractals?
HA!
I had the duct tape on before I opened this thread!
Now pardon me whilst I collect the bits and pieces.
And while I do that RG, Check out Pete Towsends Lifehouse Chronicles.
He gets into the Music Of Spheres and then some.
Or maybe it was just LSD.:-2
I had the duct tape on before I opened this thread!
Now pardon me whilst I collect the bits and pieces.
And while I do that RG, Check out Pete Towsends Lifehouse Chronicles.
He gets into the Music Of Spheres and then some.
Or maybe it was just LSD.:-2
fractals?
welcome to rr fractals................what? you mean this isn;t a new member? oops.....:p
fractal sounds like a critter off of sesame street......
fractal sounds like a critter off of sesame street......
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nvalleyvee
- Posts: 5191
- Joined: Thu Apr 21, 2005 8:57 am
fractals?
RedGlitter;548126 wrote: This may be stupid, but how do fractals work? I've looked it up online and it's always gobbledegook to me. I am poor at math and I understand it's a math thing but is there a way for a math dummy like me to understand how math becomes a design?
OMG!!! BTS knows a lot about fractals...................I'll send him this.
OMG!!! BTS knows a lot about fractals...................I'll send him this.
The growth of knowledge depends entirely on disagreement..........Karl R. Popper
fractals?
There is something lyrical about the infinite patterns within patterns within fractals. Just surreal and amazing.
Attached files
Attached files
"Life is too short to ski with ugly men"
fractals?
Nothing helpful to say from me but wanted to comment, really interesting subject, enjoying reading it.
fractals?
AussiePam;549893 wrote: There is something lyrical about the infinite patterns within patterns within fractals. Just surreal and amazing.
A truely awsome picture.
Doesn't look like it's from the Mandlebrot set, is it Julia?
A truely awsome picture.
Doesn't look like it's from the Mandlebrot set, is it Julia?
fractals?
Bryn Mawr;549917 wrote: A truely awsome picture.
Doesn't look like it's from the Mandlebrot set, is it Julia?That's a Blake.
Doesn't look like it's from the Mandlebrot set, is it Julia?That's a Blake.
Nullius in verba ... ☎||||||||||| ... To Fate I sue, of other means bereft, the only refuge for the wretched left. ... Hold no regard for unsupported opinion.
When flower power came along I stood for Human Rights, marched around for peace and freedom, had some nooky every night - we took it serious. [Fred Wedlock, "The Folker"]
Who has a spare two minutes to play in this month's FG Trivia game! ... My other OS is Slackware.
When flower power came along I stood for Human Rights, marched around for peace and freedom, had some nooky every night - we took it serious. [Fred Wedlock, "The Folker"]
Who has a spare two minutes to play in this month's FG Trivia game! ... My other OS is Slackware.
fractals?
spot;549929 wrote: That's a Blake.
That's cheating - it's fractal like :-6
That's cheating - it's fractal like :-6
fractals?
Grin.. Yes, I just grabbed the first one I saw.. kinda on the run. Not a true fractal, but nice. The local Science and Technology Museum here had an evening on fractals - the science of chaos theory and all that jazz. I freaked out with joy. :sneaky:
(My Dad was a mathemetician - most of it didn't rub off on me, but just occasionally... )
(My Dad was a mathemetician - most of it didn't rub off on me, but just occasionally... )
"Life is too short to ski with ugly men"
fractals?
AussiePam;550017 wrote: Grin.. Yes, I just grabbed the first one I saw.. kinda on the run. Not a true fractal, but nice. The local Science and Technology Museum here had an evening on fractals - the science of chaos theory and all that jazz. I freaked out with joy. :sneaky:
(My Dad was a mathemetician - most of it didn't rub off on me, but just occasionally... )
Beautiful all the same, thank you.
(My Dad was a mathemetician - most of it didn't rub off on me, but just occasionally... )
Beautiful all the same, thank you.
fractals?
Animated fractal
"If America Was A Tree, The Left Would Root For The Termites...Greg Gutfeld."