We are going to talk about fractals first, because understanding something about fractals will help with dendrimers. If you are already an expert about fractals and would like to skip straight to dendrimers then click here
Fractals are shapes that show self-similarity across scale. This sounds like a really complicated idea, but is actually quite simple.
If you look
at a tree, especially when it's got no leaves, you can see how it
branches from the trunk, but each of these branches divides into smaller
branches, and these divide into twigs. The way it divides up at each of
these points looks very similar if you just sketch that part of it, but
obviously the trunk is bigger than any of the branches, and the branches
are bigger than the twigs.
If you imagine that you are an ant, so you can't see the rest of the world, the only thing about the tree itself that tells you where you are on it is the size of the piece that you are crawling over, as the shapes are similar at each point, just bigger or smaller.
This idea of the shape being (roughly) the same, but the size being different is exactly what the phrase 'self similarity across scale' means. The idea of being roughly the same is also important, the shapes have to be similar across scale, not identical, although many artificially generated fractals are identical across scale.
Although there are many sorts of fractals in nature, they were
discovered in a more mathematical context. In fact probably the most
famous fractal is the Mandlebrot set. Even if you've never heard of it,
you've probably seen a picture of it somewhere. The images to either
side are parts of the Mandlebrot set.
Although the Mandlebrot set is generated
mathematically, it produces many beautiful and almost natural shapes.
Describing how to make your own Mandlebrot set is a bit complicated for
most of us, but if you would like to know more about it, and some more
about fractals this site is quite good.
Actually there are some other quite well known fractals such as the Koch snowflake and fractal trees which, as you might guess from their names, closely resemble natural features.
Although the rules can be quite hard to describe mathematically, they are quite easy to explain in words.
To make a Koch snowflake you start with a Koch curve like this one.
You then replace each of the four straight lines (which are
all the same length) with the original shape scaled down, and at each
generation (or iteration) you do the same. This will give you a family
of 'curves' like this.
To make a snowflake you simply start
the process with an equilateral triangle, and your first move is to
replace each of the sides by the Koch curve.
Fractal trees are even easier to explain. You start with a 'trunk' or a straight line, and at one end (usually the top) you draw two (or more) lines out from that trunk. At the end of each of these, you draw the same number of branches again, and you keep repeating. Although it is possible to do this with the branches all the same length, if you halve the length of the branches each time (and stop when you get down to a lower limit of length that you choose) you quite quickly get something that looks like a tree. In fact if you do this with 4 branches at each point it looks very like some African trees, and if you do it with 6 branches it looks a lot like a head of cauliflower or broccoli (depending on what colour you make the branches).
You can programme a computer to do many of these sorts of processes, and in fact, all the CGI effects that are used to generate scenery, landscapes, clouds and the like use a fractal model at their heart. This doesn't mean that your computer games are generating fractals each time you play, someone else has made them and then saved the images that they use on the game. Most people at home can't run a computer programme to generate these sorts of images, although if you run a Mac with OS X and buy the Maya programme, you can use the software that was used to make the film Final Fantasy, the Spirits Within. However, there are bits of software that you can use to make some of these more geometrical fractals. You can download a programming language called LOGO, and instruct that to draw pictures for you, including fractals. You can download logo for most platforms, as well as a host of other resources to help you with logo from the ATM website, their logo pages are here and their home page is over here Just to get you started there is a logo programme that will draw some different trees that you can use over here, and there is a resource library of other logo programmes and programming tips here.
What has all of this got to do with Big Molecules?
Well there are big molecules called dendrimers that are made
up of branching molecules joined together. The picture of this dendrimer
is quite typical, and although all the letters are hard to read because
it is on its side, it does make it look more like the roots and branches
of a tree.
Dendrimers are, because of the way that they are made, self-similar. A dendrimer is 'grown' in layers (or generations, just like a fractal), usually with one layer being completely one sort of molecule, the next layer being a different sort, then back to the first sort and so on. This is why they are similar at each stage.
According to the loose definition we gave at the top (shapes which are self-similar across scale) a dendrimer might not be a fractal, as they are self-similar but on the same scale. There are some more precise definitions of fractals, and according to some of them a dendrimer is a fractal, which is why we told you all about fractals before talking about dendrimers.
Dendrimers are still at the experimental stage of development. However, there are people exploring the use of dendrimers for delivering drugs to specific targets within the body (like cancer cells for example) and…
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