and i would never have thought i’d say that in a million yrs. we had a maths meeting on monday, and this is one of the take-aways i had from that meeting.
this diagram below is made purely by assigning colours to different numbers in a set. (set notation and stuff like that remember?)
difference is, there’s alot more types of sets. the pic above is made from Mandelbrot set.
the one below is made from Julia set.
dont ask me the maths behind it, cos i tried to read and understand, but i couldnt.
so what are fractals? its actually the repeated patterns formed by broken parts of the same patterns. it actually follows a specific number pattern. and different sets have different types of number patterns, with different colours being assigned to the numbers that result from the number patters, resulting in different images.
if you go to wikipedia, you’ll find animations that help you to understand.
this one shows the Koch snowflake.
this one shows you the depth of a fractal. it’s basically zooming into a specific section of the pattern, and then further zooming in and so on.
occurs in nature. this is a fractal version of a Romanesco broccoli.
for those who know, many other things in nature follow patterns too. number patterns.
the fibonacci sequence generates the following numbers: 3, 5, 8, 13, 21, 34, 55, 89…… so whats the pattern?
each number is the addition of the previous number, to put it simply.
the fibonacci sequence is seen clearly in sunflowers.
the number of petals are always numbers from the above pattern. the spirals you can observe in the middle of the flower are also consecutive numbers from the fibonacci sequence.
cool eh! the beauty of maths!
though of course, to create something like this, you’d need to dwell deep into the mathematics of mathetics…. usually learnt at higher levels… and can get rather dry, unless you really have the interest…