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# Fractals watch

1. Basically I'm doing an extended project on fractals. I've been trying to find books on how to construct fractals or perform computations relating to them (I will be trying to create my own fractal using Microsoft Excel). Does anyone have any suggestions? I'd aso like to read books that explain how fractals are used in real life situations, like for working out the surface area of things with irregular shapes or something like that. I've tried to find some books on Amazon, but the descriptions and the reviews are not really that helpful.

Thank you.
2. http://en.wikipedia.org/wiki/Mandelbrot_set (look at the definition for a Mandelbrot set for some stuff to compute)

You might also want to mention how long the coastline is.
3. (Original post by SimonM)
http://en.wikipedia.org/wiki/Mandelbrot_set (look at the definition for a Mandelbrot set for some stuff to compute)

You might also want to mention how long the coastline is.
Thanks for your help. Any ideas of books that I can read though? Also, I've never created a program or anything before, so all that stuff looks really complicated to me. Are there any books that can help me with that?

Thank you.
4. (Original post by rapha)
Thanks for your help. Any ideas of books that I can read though? Also, I've never created a program or anything before, so all that stuff looks really complicated to me. Are there any books that can help me with that?

Thank you.
what exactly is this project?
5. (Original post by Totally Tom)
what exactly is this project?
Well, the title of the project is 'Exploring fractals and its real life applications'. I will be looking at how fractals are used in real life and the steps to designing a fractal. Then I'll have to create my own fractal using Microsoft Excel. But first, I need create a program in Excel (if that even makes sense) to design a fractal. My teacher who is supervising me has asked me to find a book that explains it or maybe someone who knows how to do it on excel, but so far I haven't found anything.
6. Googling on 'excel fractal' gives lots of links. How well do you know Excel? (I don't know it well myself).

Do you even have an idea what kind of fractal you want to calculate? (Sierpinski gaskets are easy in Excel, but I'm not sure I'd really consider them fractals).
7. (Original post by DFranklin)
Googling on 'excel fractal' gives lots of links. How well do you know Excel? (I don't know it well myself).

Do you even have an idea what kind of fractal you want to calculate? (Sierpinski gaskets are easy in Excel, but I'm not sure I'd really consider them fractals).
I don't know much about Excel. I can use it to peform calculations and simple stuff like that. I've never done any programming in the past. I'm trying to create something like this: http://shoresofchaos.com/Shores/downloads.htm

On this same website it says:

A further appreciation of fractals comes from generating them yourself. It is possible writing your own programs but a much easier way is using either a freeware or shareware program
I don't want to use a fractal generating software. I need to create my own. I would like to know if there are any books that can help me with this.

Thank you.
8. I don't know much about it, but someone that did Art GCSE mentioned it to me, but Apophysis, which I think you can get a free download off google for, is a program for rendering (and I think programming) fractal patterns. It could be worth looking into, but as I said, I don't know much about it, so perhaps someone else could advise further.
9. (Original post by GHOSH-5)
I don't know much about it, but someone that did Art GCSE mentioned it to me, but Apophysis, which I think you can get a free download off google for, is a program for rendering (and I think programming) fractal patterns.
<disclaimer: I've only had a quick look at it>.

There's a scripting language, but I'd be really really uncomfortable saying you can actually program with it. And (obviously), it's not Excel.

Excel is a problem, to be honest. Stating the obvious, it's not designed for creating fractals. So you're going to end up having to do a few tricks to persuade it to do what you want. At which point you need better Excel skills than most people are likely to have. (I'm roughly at the level where I could calculate and display a Mandelbrot using Excel, but I wouldn't know how to make it easily reset and recalculate again. That is, it wouldn't be repeatable).

If I was a teacher wanting people to learn how to program fractals, I think I'd go with either Python or Ruby. I'd probably get people to output images as straight ASCII PPM, and then provide them with a converter program to convert PPM to something useful like BMP or JPEG. I don't know if something like that is an option here.
10. (Original post by DFranklin)
There's a scripting language, but I'd be really really uncomfortable saying you can actually program with it.
Fair enough. I've not actually done any programming myself, so I wasn't aware of the difference between a scripting language and programming
11. (Original post by DFranklin)
I'm roughly at the level where I could calculate and display a Mandelbrot using Excel

I'm amazed that this can be done. That probably just shows my ignorance of Excel. Would you mind outlining how it could be done?
12. (Original post by DFranklin)
(Sierpinski gaskets are easy in Excel, but I'm not sure I'd really consider them fractals).
A bit off-topic, but why not?
13. (Original post by rnd)
I'm amazed that this can be done. That probably just shows my ignorance of Excel. Would you mind outlining how it could be done?
When it comes to writing it out, I realise it's more complicated / tedious than I thought. So I don't guarantee this will work, but I'm sure I could make it work without too many changes.

For sake of argument, lets say our resolution is 40 x 40 cells. The mandelbrot iteration is z->z+c, where z and c are complex.

Set up two arrays of size 40x40(probably makes sense to put each array on separate pages) so that the values in the first array go from -2 to 2 in steps of 0.1 as you go along in columns (these are basically going to be the 'real' values), and the values in the second array go from -2 to 2 in steps of 0.1 as you go along in rows (there will be the complex values).

Set up another 3 arrays with values that are all set to zero. We'll use two of these to hold the real and imaginary parts of z, and one to hold the number of iterations.

OK, now we need to do the actual iteration.
If z=x+iy, c = a+ib, then the new values of x, y are (x*x-y*y)+a, 2*x*y+b
So we can calculate the new values for z and stick them into two new arrays.
Then we copy the values from those arrays back into the original arrays for z. (We have a circular dependancy at this point, and I'm not 100% sure how you'd make sure Excel does what you want. Worst case, we can implement a "ticker" that simply goes up by 1 on each recalculation, and then do the 'calculations' on odd ticks and the 'copies' on even ticks).
Similarly, we use a conditional increment on each cell in the array holding the iterations, so that we only increment the iterations for a cell if 'z' for that cell has modulus < 2.
Then you simply keep pressing F9 to recalculate until you've done enough iterations.
To 'render' the result, you can use conditional formatting to colour each cell depending on the number of iterations.
14. (Original post by Scipio90)
A bit off-topic, but why not?
More 'philosophical' than anything else, but the "easy" way of calculating them in Excel isn't really using their fractal nature at all. (You just render according to whether the entries in Pascal's triangle are odd/even). So you're not using self-similarity, or an iterative process, and the way you do it has nothing to do with how you'd normally render a fractal.

In other words, it's not that they're not a fractal, but that if someone uses them as an example of calculating a fractal, it's a really bad (atypical) example.
15. Does anyone know of any good books that give a clear introduction o fractals? I've only just finished my first year of college, so not something too difficult to understand.

I was thinking of this book because it also talks about the applications of fractals.

Thank you.
16. (Original post by DFranklin)
When it comes to writing it out, I realise it's more complicated / tedious than I thought.....
Interesting. Thanks. I might have tried it but as you say, it does look a bit tedious (and I'm still not certain I could tackle it).

Could be useful for someone doing a project on fractals using Excel though.
17. (Original post by rapha)
Does anyone know of any good books that give a clear introduction o fractals? I've only just finished my first year of college, so not something too difficult to understand.

I was thinking of this book because it also talks about the applications of fractals.

Thank you.
"Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry."

I really don't see what your teacher is expecting you to come back with. Most of what you'll find on fractals will probably go over your teachers head. I see it as being a pretty ridiculous task.
18. As I've already said to the OP (via PM), this is an area where the textbooks all tend to be pretty technical. Conversely, there are lots of reasonably accessible articles on the internet, if you just "want to make a fractal".

To be honest, I think at this point rapha ought to go back to his teacher and say he needs help.
19. Do you think they would mind if I said I wanted to change my project title? I'm worried it might be too late as we have already filled in the project proposal and got feedback from it. I wanted to do something on infinity at first, but then my teacher said I should choose a more 'narrow' topic. He suggested fractals, it sounded interesting so I chose to do it. I'll try and talk to him tomorrow. Thanks guys.
20. fractals are a really interesting topic. and if you are willing to learn (or at least copy) a little java it is quite easy too - there must be loads of fractal guides on the internet

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