The Mandelbrot Set
In my last post about the mandelbrot set I said:
I would put the Mandelbrot explorer script online however it is very computationally intense. It takes around 5 seconds to generate 1 image.
Now I have created a new explorer which you can use.
Yesterday as you are probably well aware was April Fool’s Day. Google as ever produced a range of April Fool’s jokes, this year based around an artificial inteligence system called CADIE. My favourite joke was the 3D chrome browser.
Knowing about how 3D images are produced I knew that Google couldn’t possibly render whole pages in real 3D. Instead it uses a clever rendering effect to create two identical images of the page and convert one into the red component and the other into the blue and green component. Read the rest of this entry »
Fractals are some of the most intriguing shapes. The Mandelbrot set is one of the most intriguing fractal sets. To be honest with you I don’t really get what it represents and why it has such a weird shape but I know that it is intriguing to see.
For those mathematical boffins the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0=0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. Read the rest of this entry »
Father’s day was celebrated here in the UK last Sunday. I decided that I’d rise to the occasion and make something special. I can’t say that I’m a whiz with Photoshop because I don’t actually own a copy of it, instead I rely on a rather old version of Paint Shop Pro.
Paint Shop Pro is a nice application. It lacks some of the more advanced canvas and brush features of Photoshop which means that it lacks the creative edge. Also I have yet to find a way to convert Photoshop brushes and documents to Paint Shop Pro documents.
Read the rest of this entry »
Steganography is what I would call the less powerful and less well known brother of cryptography. Whereas cryptography is encoding something so it can’t be read without a key, steganography is hiding something so it can’t be found without directions. Since cryptography offers a greater level of security for less effort it has often been used as opposed to steganography.
Think of cryptography as the lock to a safe. You need a key to open the safe. Steganography is hiding the safe somewhere where it can’t be found easily such as behind the painting on the wall. To find the safe you need directions. So how is steganography useful in the modern world. It can actually be used in several ways. A secret file can be hidden on your computer so it looks like an ordinary file. I’m going to show you today how to hide an MP3 file inside a JPEG or GIF image.
Read the rest of this entry »