[Jprogramming] Mandelbrot

[Devon McCormick]

Here's a start (probably based on Gene McDonnell's (?)) old sig of a few
years back:

NB. Make 361x600 matrix of complex numbers.
   $ary=. (159%~i:_180) j.~/ 230%~_480+i.600
361 600

NB. Sum the squares of this matrix, recursively,
NB. 10 times; takes less than 1 second.
   6!:2 'resultIter=. ((+*:)^:10 0:) ary'
0.97362

NB. Bucket the results according to how many are
NB. greater than each of 0 through 15.
   clr0=. +/(i. 16) </ |resultIter

NB. Count how many in each bucket.
   +/ (,clr0) =/ i. 16
2 68576 5547 1662 997 709 496 401 380 298 275 212 192 200 144 155

NB. Sum squares, again 10 times, of previous
NB. result: takes less than 2 seconds.
   6!:2 'resultIter=. ((+*:)^:10 0:) resultIter'
1.76382

NB. Again, bucket results to give us next layer of
NB. colors: clr1.
   clr1=. +/(i. 16) </ |resultIter    NB. Repeat this whole process 4 more
times.
   6!:2 'resultIter=. ((+*:)^:10 0:) resultIter'
2.07477
   clr2=. +/(i. 16) </ |resultIter
   6!:2 'resultIter=. ((+*:)^:10 0:) resultIter'
2.04566
   clr3=. +/(i. 16) </ |resultIter
   6!:2 'resultIter=. ((+*:)^:10 0:) resultIter'
2.04578
   clr4=. +/(i. 16) </ |resultIter
   6!:2 'resultIter=. ((+*:)^:10 0:) resultIter'
2.04922
   clr5=. +/(i. 16) </ |resultIter

NB. Notice how distribution keeps shifting left:
NB. as successive iterations push more points to
NB. higher values (except for those in actual set).
   +/ (,clr5) =/ i. 16
2058 60728 51 6 2 2 2 0 0 0 1 0 0 0 2 0
   $,clr5
216600
   qts ''
2002 3 18 15 22 3.475

NB. Take a look at summary result of all 6 layers.
   viewmat clr0+clr1+clr2+clr3+clr4+clr5

Good luck - hope this is enough to get you started.

On 8/19/06, Ahmad Issa <ahmadissa at gmail.com> wrote:
>
> I don't quite have the money to get the book (i'm still in highschool),
> i'd
> really appreciate it if you could write some code that i can study.
>
> regards, Ahmad
>
...
-- 
Devon McCormick
^me^ at acm.
org is my
preferred e-mail