I have been thinking about fractals for the last few years, and found some renewed interests here in its application in social media – here are some sharing http://connectivismeducationlearning.ning.com/forum/topics/future-of-education?commentId=2749904%3AComment%3A9897&xg_source=activity
I believe that there might be some ground breaking ideas behind fractals especially in describing how it could be represented as a pattern in
(a) our brain
(b) our origins of life
(c) our way of communication and networking, especially in a complex open networked environment
(d) our future of education.
Here are my meanderings:
The basis of fractals is routed from (you could watch the video series 1-6 and it was mentioned in one of them on the formula of fractals basis https://suifaijohnmak.wordpress.com/2010/03/30/the-map-is-the-treasure/
f(Z)= Z x Z +C where Z is a complex number (a+bi) – where a and b are real numbers and i is the square root of -1, an imaginary number. I include this as a brief background only, and I must admit that I am too new to it. 🙂 Sorry Jenny I don’t want to fill you with jargon of mathematics, but this is important to understand. And Roy and Matthias, please point out if I am wrong in any of the interpretation. I love to learn more on this.
This is similar in concept to the Newton’s iteration equation in solving numerical problem, which is also fundamental in computation using iteration.
Relating again on the video https://suifaijohnmak.wordpress.com/2010/03/30/the-map-is-the-treasure/ development of fractals based on just the growth of two lines (could be both equal in length, or unequal, with same or different directions) is fascinating, as this may provide some cues in lots of areas:
(a) Our brain. First, I suspect that the development of dendrites in the nerve cells and the connections are formed could be simulated using the fractals development pattern. I don’t know if there are any simulation based on that, but surely the full brain scan provides a pattern that could be studied in greater details, to see how such “fractals” are formed and developed. I realise patterns of fractals appear when I wash my hairs with hot water, and such images of fractals could be “visualised” naturally. Have you got similar experience?
(b) Origins of life. I have written an article (never published) back on 22 November 1997 at 11:36 pm. Here is part of it (though some other parts have been added/revised now):
A basic mathematical theory on the multiplication of cell.
(details not shown)
As life begins in the multiplication of cells:
Imagine a round cell is now sub-divided into two identical cells of the same size as the original one.
The surface area of the multiplied cells could be equal to the surface of another cell of radius r2
By equating 4x pi x r2xr2 = 2 x 4 x pi x r1 x r1
r2 = square root 2 x r1
This suggest that the cells increase by square root 2 the original size of the radius but two-folds in area for any division of cells.
The formula f(Z) = ZxZ +C could be a general formula for explaining this division of cells (I don’t think I have learnt anything about fractals in 1997, and I just made up that formula to prove my point in the division of cells). So, when I watch the video now and realise that the same formula was used in fractal formation, I was so amazed. I am just not sure where I got that idea from. Remember in 1997, the Internet wasn’t popular as yet, and I don’t think I knew the formula as mentioned in the M-SET.
But I really did a lot of original work without referencing to any literature.
Let Z be a complex number denoted by a+bi, you could derive that
C=square root 2 x a (working not shown here)
If we apply this principle to the multiplication of basic cell, it means that one cell will be divided into two, and the two cells will be divided into four and so onwards.
It seems that the square root of 2 is the mysterious figure that should be investigated. And I suggest that this is fundamental “number” that could unfold the origins of life – i.e. square root 2. That is, if we keep squaring root the 2 objects, then it would become 1.
This is similar to the concepts of uniting the sperm and ovary in human birth, where the ovary will begin to subdivide once the sperm unite with ovary. So the sperm is C and ovary is Z, where the ovary multiplies when the sperm entered into the equation, and the life begins. Does it make sense?
(c) way of communication and networking, especially in a complex open networked environment. I have written a post on this – the map is the treasure
(d) our future of education. Given the current trend, could we predict the future using fractals as pattern? May be. I am still pondering on this, but I would postulate Z (future education) = Z (present education + imaginary or predicted condition of education) x Z (present education + imaginary or predicted condition of education) + C (paradigm shift: based on networking, social media and technology affordance, and promotion and support from government, institutions, communities, local and global networks, social medias etc.)
The following is just my intuitive thoughts only.
Finally, assume that a is our present life, b is our future life (imaginary) in the Z=a+bi then if our present life is “equated” to our future life, then we will have eternal life (as a Catholic, that is a teaching by Jesus Christ). The eternal life could also be a reality by applying the principle of multiplication of cells. Also our faith will multiply as a multiple of two just as the cell division. This is also how religious beliefs gain its life in its spread of good news, IMHO.
Hope you don’t mind me sharing these really “strange thoughts” with you, but I could assure that you would never find it in any literature, as I made all these up myself.
I am posting it here onto my blog, though such are just half-baked ideas, not yet ready for “cooking”.
Let me know what you think, and Roy please, as I know you would also like something new and novel, as a discourse scholar, and Matthias as a brilliant Mathematician, and Jenny, as a critical thinker and scholar.
Please fill free to share in the Ning or your blog or your wikispace (Roy) too.
Wishing you all an enjoyable Easter Holiday.