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Read. That how I do it. I'm also 17. I also don't understand university
level algebra, calculus, chaos theory, cosmology or super string theory (I
understand a little about cloth in general, though). I just read, ask my
teachers and by trial and error something comes up that's worth showing.
Basically, I just know that the attractor image I made has something to do
with chaos, how and why are not of my concern, just making the cool image
is. (=
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You can teach yourself anything you can take a course for. A structured
environment makes it easier (a little), but if you can learn to structure
your habits of learning (reading, working examples, etc), then class time is
not required.
Of course, there isn't any system of correcting learned mistakes this way,
but it can be done.
Too, reading isn't everything. Case in point. I know someone who studied
to become a doctor (Phd) of Aerodynamic Engineering, and I know someone else
that spent the same amount of time flying, reading for interest, and
building airplanes. I'll let you guess which one knows the subject best and
makes fewer mistakes. :)
That sheepskin comes in handy, though!
GrimDude
vos### [at] arkansas net
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One of my goals is to create a Cyclopedia for POV-Ray for speceific q&a and I
suspect that you have questions that will work. If you post your exact
question I will post an explanation and solution. If someone else finds a
solid solution, I will post that with my own explanation about the whys and
wherefores. I tutor folks with college level algebra, which is the same stuff
as high school level classes.
My goal is to make you understand what is happening and why, and I also strive
to make it clear and presentable (unlike some of my posts to this NG), so if
something isn't clear, ask away.
The site doesn't have much of anything at this point, but please help me fill
it up. I can't begin to guess at the questions you will ask, but once you ask,
I can answer.
The site is currently at
http://www.spiritone.com/~english/cyclopedia/cyclopedia.html and if it's
unreadable, accept my apology. I'm experimenting with CSS and trying to find a
comprimise between how all the other browsers draw this stuff is quite a
challenge... I'm working on that, too.
Josh
Thomas Lake wrote:
>
> Well I've been reading/posting/replying to this newgroup for some months
>
> now and I have always been interested in and even more so now, with the
> advent of all these fractal images, the more mathematical and technical
> sides of pov-ray. I've always wanted to know how people create these
> amazing fractal patterns and neat abstract shapes many of which are
> featured in the examples that come with Pov-Ray. Also I am VERY
> interested in learning how to create my own Macros, just for the fun of
> it, I have endless ideas for macros, most of them useless but fun
> anyway. What I'd like to know is just where should I start to learn any
> of this? I know almost no programing, well a little JavaScript, and I
> don't know any math beyond very basic algebra. Now I have played around
> with some simple fractals, like the examples which come with Lparser,
> and I even began to start to understand them but only very basically. If
>
> anyone could point me to any good resources for a beginner in these
> areas, i.e. macro's and fractals, I would be very appreciated. Oh and
> please keep it simple, I'm 17 and therefore don't understand and
> university level algebra,calculus,chaos therory,cosmology or super
> string theory. :-)
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Hello.
I would suggest a little of what both TonyB and GrimDude were saying. What I
know, and what I'm learning I've taught myself - via the hard works of
others that have been recorded in print - i.e. I read a lot! Along with the
reading I apply apply and apply some more. This is good to do if you really
want to learn and believe you have the diligence to and hunger to climb an
ever rising mountain. To be honest, this is the same attitude you must have
to succeed in University. No one there is going to nor be able to spoon feed
your education. You must read, study and apply to reap any benefit and
reward from your efforts. Going to University is necessary if you want
documentation to prove your knowlege so that it can be applied toward a
career path. However, if this isn't a career choice yet you still want to
learn and discover then documentation isn't that important and the pace you
set can be as comfortable and challenging as you wish. So, prelude over: My
advice would be used book stores and garage sales - cheap books - very cheap
and the Web. There are thousands of resources all relating to the topic of
math, for free, and hundreds of sites run by people who want only to share
their knowlege and help anyone who is like-wise interested. So, I would
recommend getting your hands on a book of advanced algebra - or if you are
past that - Trig - and start on page one. Be patient, consistent - and never
look at the bibliography until you have finished the book (it will only
scare and/or distract you ) ;-]
KB-
p.s remeber - apply, apply, apply; do the problems answer the questions -
banking from GrimDudes message - experience will always pay-off greater than
anything else - and experience is something "done" not "going to do".
Thomas Lake wrote:
> Well I've been reading/posting/replying to this newgroup for some months
>
> now and I have always been interested in and even more so now, with the
> advent of all these fractal images, the more mathematical and technical
> sides of pov-ray. I've always wanted to know how people create these
> amazing fractal patterns and neat abstract shapes many of which are
> featured in the examples that come with Pov-Ray. Also I am VERY
> interested in learning how to create my own Macros, just for the fun of
> it, I have endless ideas for macros, most of them useless but fun
> anyway. What I'd like to know is just where should I start to learn any
> of this? I know almost no programing, well a little JavaScript, and I
> don't know any math beyond very basic algebra. Now I have played around
> with some simple fractals, like the examples which come with Lparser,
> and I even began to start to understand them but only very basically. If
>
> anyone could point me to any good resources for a beginner in these
> areas, i.e. macro's and fractals, I would be very appreciated. Oh and
> please keep it simple, I'm 17 and therefore don't understand and
> university level algebra,calculus,chaos therory,cosmology or super
> string theory. :-)
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GrimDude wrote:
>
> You can teach yourself anything you can take a course for. A structured
> environment makes it easier (a little), but if you can learn to structure
> your habits of learning (reading, working examples, etc), then class time is
> not required.
> Of course, there isn't any system of correcting learned mistakes this way,
> but it can be done.
> Too, reading isn't everything. Case in point. I know someone who studied
> to become a doctor (Phd) of Aerodynamic Engineering, and I know someone else
> that spent the same amount of time flying, reading for interest, and
> building airplanes. I'll let you guess which one knows the subject best and
> makes fewer mistakes. :)
> That sheepskin comes in handy, though!
>
> GrimDude
> vos### [at] arkansasnet
There are a lot of real examples to support your claims. I have worked
in engineering for years without the benefit of a formal education.
I survive by sheer cunning and a lot of common sense. I can recite
numerous examples of positions or projects I have held that were given
to engineers fresh out of college based on their credentials alone. I
can then detail the enormous amount of my personal time I had to spend
to teach the new wonder boy's the basics of the engineering discipline
being used for solving the tasks at hand. Had they left me to my duties
it could have been accomplished in a much shorter time than wasting my
time training someone who was allegedly my superior by virtue of his
scholastic training. A lot can be said for on the job experience but
little for the rewards of such experience without the credentials to
back them up.
--
Ken Tyler
mailto://tylereng@pacbell.net
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Thomas Lake wrote:
> anyone could point me to any good resources for a beginner in these
> areas, i.e. macro's and fractals, I would be very appreciated. Oh and
> please keep it simple, I'm 17 and therefore don't understand and
> university level algebra,calculus,chaos therory,cosmology or super
> string theory. :-)
In the middle of 1997 when I was up late and had nothing to do, I read
the POVray-tutorial from the beginning to the end, did EVERYTHING in
that tutorial, and started POV:ing. I don't know much math either, you
don't have to.
The tutorial is a good start.
--
// Rikard Bosnjakovic - http://a214.ryd.student.liu.se/ - ICQ: 1158217
----------------------------------------------------------------------
Before you criticize someone, walk a mile in his shoes. That
way, if he gets angry, he'll be a mile away - and barefoot.
----------------------------------------------------------------------
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The best way is to have a goal for what you want to do. Actually, I'm
having a problem doing things which are not related to learning
something new, i.e., I only think it's fun if there's some sort of
problem solving involved.
Example: I have always loved airplanes, me and my father used to build
R/C model aircraft and I was in some way raised on aircraft. Now, I love
the looks of Cessna:s and wanted to be able to model as beautiful things
as I had seen been modeled in Rhino and similar programs. I was told
about sPatch (http://www.cableone.net/alyson/spatch.html) and started
right away.
Now, I had what I needed: an idea of what I wanted to do, and a problem.
The idea was to model a Cessna, and the problem was to find out how to
do it in sPatch (=learning the program).
Pretty much the same with everything I've done, i.e. an idea, and a
problem. (I believe I would be very happy to be an inventor, but I don't
know how I would handle a situation where I was out of ideas...guess I'm
doing the right thing now as I'm getting a good education in systems
development - which allows me to get a permanent job at some company
instead.)
So just go ahead and try to realize whatever ideas you have - you will
learn a great deal in doing so.
- Mikael.
-----------------------------------------------------------------
Mikael Carneholm
Dep. of Computer Science
http://www.studenter.hb.se/~arch
E-mail: sa9### [at] idautbhbse
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Thomas
All the above advice given by others is good advice.
One thing that I would add, is don't put it off. It's much
harder to learn as you get older, and much harder to work hard
too.
Give yourself a goal and put all your energies into achieving
that goal, and don't get disheartened if you don't achieve quite
the way you would like to. We all make mistakes and that is how
we learn.
Good luck.
Steve
Thomas Lake wrote:
>
> Well I've been reading/posting/replying to this newgroup for some months
>
> now and I have always been interested in and even more so now, with the
> advent of all these fractal images, the more mathematical and technical
> sides of pov-ray. I've always wanted to know how people create these
> amazing fractal patterns and neat abstract shapes many of which are
> featured in the examples that come with Pov-Ray. Also I am VERY
> interested in learning how to create my own Macros, just for the fun of
> it, I have endless ideas for macros, most of them useless but fun
> anyway. What I'd like to know is just where should I start to learn any
> of this? I know almost no programing, well a little JavaScript, and I
> don't know any math beyond very basic algebra. Now I have played around
> with some simple fractals, like the examples which come with Lparser,
> and I even began to start to understand them but only very basically. If
>
> anyone could point me to any good resources for a beginner in these
> areas, i.e. macro's and fractals, I would be very appreciated. Oh and
> please keep it simple, I'm 17 and therefore don't understand and
> university level algebra,calculus,chaos therory,cosmology or super
> string theory. :-)
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Mikael Carneholm wrote:
> Pretty much the same with everything I've done, i.e. an idea, and a
> problem.
That's the idea with all problems: Focus the problem, fetch available
datas, check available tools for solving, do solving.
(Off topic: George Polya's book 'How to solve it' is a goldmine for
problemsolvers)
--
// Rikard Bosnjakovic - http://a214.ryd.student.liu.se/ - ICQ: 1158217
----------------------------------------------------------------------
Before you criticize someone, walk a mile in his shoes. That
way, if he gets angry, he'll be a mile away - and barefoot.
----------------------------------------------------------------------
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Regarding fractals it is easy. You see there are only 4 people in the entire
world that really understand the fractal fomulae and 1 of them is dead. What
happened is that these 4 people discovered these cool fomulae and showed
them to other people. Those other people then started playing with them and
tweaked a few values or whatever and then said they'd invented a new
fractal. Take for example the Mandelbrot fractal. There are about 2
gazillion variations on that one fractal. People try to make it 3d or 4d or
5d or whatever and they all claim they invented a new fractal. Not only is
that not true but no one really understand the Mandelbrot in the first
place, not even Mandelbrot himself. Here is how it happened:
One day Benoit Mandelbrot was playing with numbers on a sheet of paper and
started with this:
1 = 1
He knew this was boring so changed it to:
x = 1
This wasn't much better so how about:
x = 1 + 1
but since that is the same as x = 2 he livened it up with:
x = 1 + y
but since that was just a static equation and really didn't go anywhere he
decided some reiteration would be nice:
x = x + y
still this wasn't too interesting, specifically it was too predictable so he
changed it to:
x = x^2 + y
the problem with this was that it would grow too large too quickly for any
normal number, but what about abnormal numbers, specifically imaginary
numbers? so Benoit said that x and y would be imaginary numbers, he also
changed them to z and c. C is for constant and z if for the letter after y
since it is usually plotted on a x-y grid. So that gave him:
z = z^2 + c where z and c are imaginary numbers
Finally in order to make the plot he said that the x coordinate of the grid
would be the real part of c and the y coordinate would be the imaginary part
of c and that z starts out as zero. How do you determine which color to plot
each pixel? Simple, just count how many times you iterate the equation and
as soon as Z goes off to infinity use the number of iterations up to the
point as the value (color, height, transparency, or whatever) for that
pixel. Of course in a typical M-set plot the value of 4 is used for infinity
during this check (4 == infinity? where the heck'd that come from?).
Now, do you really think Benoit actually understood what he was doing? OF
COURSE NOT, it was all doodles on a peice of paper that happened to come out
looking interesting. You never hear about another mathematician named
Charles Brottlemand, that's because his doodles just turned out as a big
dark ugly brown circle, no one was intersted, it wasn't colorful like the
M-set.
Sorry for the digression. What I said above was about 1/2 serious. Most
people that do stuff with fractals don't really understand them, they just
copy and play with the formulas. The best way to learn is to play. Take a
fractal formula and plot it. Then change some values and plot it again. With
POV you can do some cool things by changing values as you progress along an
axis and then you get a 3D fractal. Likewise you can make a 4d fractal
(i.e., animation) by rendering lots of scenes with parameters changing a bit
each frame.
--Rainer
P.S. For more info on the M-set check out
http://www.cygnus-software.com/theory/theory.htm
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