Verlet integration in Haskell

Verlet integration algorithm written in 3 minutes

-- Verlet integration

projOneTwo ( a, b, c , d ,e ) = ( a, b)

nextStepInt (_ ,_ , 0 ,_ ,_ ) = []

nextStepInt ( xt ,vt , n , acc , h ) =

let

atph = acc . ( xt + ) $ h

vtph = vt + atph * h * 0.5

xtph = xt + h * vt + 0.5 * acc xt * h^2

in

( xtph, vtph , n-1 , acc , h ) : nextStepInt ( xtph, vtph , n-1 , acc , h )

timeInt ( xt ,vt , n , acc , h ) = map ( projOneTwo ) $ nextStepInt ( xt ,vt , n , acc , h )

example ( spring ) :

timeInt (0 , 1 , 10000 , (\x -> 0.1 * ( - x ) ) , 0.2 )

my delicious

now i'm in delicious: http://delicious.com/koteth

A lot of Haskell links.

Cairo-Chaos Haskell

Haskell chaos and lib-cairo.

Is only a fixed-point iteration over this function:

lgs x r = r * x * exp(- x )

Dollar $ operator in Haskell

Do you know what is $ operator in Haskell?
$ means simply , 'apply the left function at the right value'.

f $ x := f x

it seems really trivial, isn't it ?
But, for example in this kind of situation, is really usefull:

zipWith ( $ ) ( cycle [ \x -> div (x + 1) 2 , \x -> div x 2 ] ) [1..]

here you have a infinite list of function:

a = cycle [ \x -> div (x + 1) 2 , \x -> div x 2 ]
( ie: [\x -> div (x + 1) 2 , \x -> div x 2 , \x -> div (x + 1) 2 , \x -> div x 2, ... ] )

and you want to apply every element of the list at the element
at the same index in the second list:

b = [1..]

zipWith, for every index i takes the element a(i) of the left list
and b(i) of the right list and execute what is requested inside the parentheses.
In this situation is specified $ so:

a(i) $ b(i ) := a(i) ( b(i) )

the result must be the following:

[ 1 ,1 , 2, 2 , 3 ,3 ... and so on.

Prime Numbers in haskell

well, do you want to know how to find 'prime numbers' in a quick and dirty
way using Haskell ?
try this!

import Data.List
nubBy ( \x y -> mod y x == 0 ) [2..]

Haskell is so easy and charming...

( ps: if you want to speed up a little bit:
nubBy ( \x y -> ( x*x-1 <= y ) && ( mod y x == 0 ) ) [2..]
)

re: Mandelbrot Set in Haskell

import Data.Complex

conv p=(\n->".,:;|!([$O0*%#@?"!!(n-1))(ceiling (p*8)::Int)

gr=map(\y->[(x:+y)|x<-[-2,-1.97..0.7]])[-1.2,-1.13..1.2]

--px w=magnitude(foldl1(\z c ->z^2 +c)(replicate 10 w))

px w=(magnitude.last.take 10.takeWhile(\r->(magnitude r )<6).iterate(\z->z^2+w))w

image=map((map(\el->case(px el<2)of{true->conv(px el);_->' '})))gr

main=mapM_ putStrLn image

better...

Mandelbrot set in Haskell

import Data.Complex
gr = map(\y-> [( x:+y )|x<-[-3,-2.95..1]])[-2,-1.9..2]

px (a:+b) = magnitude(foldl (\z c ->z^2+c) 0 (take 10([((a*x):+b)|x<-[1,1..]])))

image = map((map(\el->case(px el<2)of{true->'*';_ ->'-'})))gr
main = mapM_ putStrLn ( (map(\el->show el) )image )

A first interpretation ( a little bit unsatisfactory ) of the Mandelbrot set in Haskell

Numbers in Haskell

The core of numbers post in Haskell:

idens p q x = case ( rem ( x ^ 2 ) p ) of { 1 -> 1 ; _ -> 0 }
numList p x = map ( idens p x ) ( map ( x * ) [ 1..( p-1 ) ] )
matIde p = map ( numList p ) [ 1..(p-1) ]

The Path of St. Augustine

Here you can find info about "Il Cammino di Sant'Agostino ( The Path of St. Augustine )" in Italy.

Dungeon ( Quinta da Regaleira - Portugal )

Quinta da Regaleira

( Mystic Cristina )

Mandelbrot in Rebol

And this is my interpretation of Mandelbrot fractal using Rebol:

mandelb.r

This language allow to write a gui using few rows of code.

There is still a problem with zoom functionality ( I hope to fix it soon ).

You can see also my ruby mandelbrot .

Latent Semantic Indexing ( LSI )

LSI is a simple but powerful indexing and retrieval method that is able to identify patterns in the relationships between the terms and concepts contained in a text corpus.

The mathematics of LSI easy to understand cause is based entirely on vector and matrix algebra.

I'll post soon some code ( if someone needs code, my mail is always open ).

A good link to start your journey is: lsi.research.telcordia.com/lsi/LSIpapers.html .

Peano in Js

You Can find Here 'peano', my interpretation of Peano Curve in jQuery ( javascript ) using canvas ( if you insist to use iexplorer you must download also exCanvas.pack.js to see something ).

To see this image you need only the last jQuery js library and a browser...

Ah, you also need to rename the file with 'HTML' as extension.

Metamorphosis ( Music animation )

Follow this link...

http://vimeo.com/1747316?pg=embed&sec=1747316

context-free art

A little piece of context-free art:

circles.cfdg

startshape trails
background {b -1}
rule trail {
trail{
sat 0.001
a -0.001
r 0.4
y 0.5
s 0.999y 0.5
}
SQUARE{s 1}
}
rule trail 0.001 {
trail{flip 90} ring{x 5}
}
rule trails {
140*{r 120}trail{b 1 sat 0 h 100}
}
rule ring {
120*{r 5}SQUARE{s 4 0.5 y 6 h 100}
}

Rebol Search File

Another little Rebol program:

rebTest.r

REBOL [Title: "Ricerca"]
mainWin: layout [
banner green "Ricerca Parola" box brick 580x2
text "Parola da cercare"
infi1: field infi2: field ""
text "nome file"
selFile: text-list data read %. [
infi2/data: value
infi2/text: value
show infi2
]

 button "Ricerca"  [
fil1: to-file infi2/data
text: read fil1
outOne: copy ""
while [ text: find text infi1/data ] [
   formattedStuff:  reduce [ " ( " index?  text  " ) " copy/part text  10  ]
append outOne "^/ ( indice ) riga:   "
append outOne form formattedStuff
text: next text
]
tuno/text: form outOne show tuno
]
at 260x70
tuno: area 340x300 across
text "Risultato"
]
windowHelp: layout [
backcolor linen
h2 "Help Window"
text 300 { Inserisci la parola da ricercare e il nome del file...
}
button "Chiudimi" [ unview/only windowHelp ]
]

windowHelp/offset: mainWin/offset + (mainWin/size * 1x0) + 10x0
view/new mainWin
view/new windowHelp
do-events

'Text Categorization with SVM

A really nice pdf about 'Text Categorization with Support Vector Machines' ( from University of Dortmund ) :

http://www.cs.cornell.edu/People/tj/publications/joachims_97b.pdf

I'll try to post soon some code in Python about this problem...

My first time in Rebol and numbers

Rebol is a fantastic language!
You can try this code in the Rebol/view Console:
numbers.r

REBOL [Title: "Numbers Test"]
ena: 121
positions: []
dimPal: 3

unitar: func [ ele enne ][ either (( (ele // enne) == 1 ) or (( ele // enne) == (enne - 1)))[ 1  ] ["-"] ]

evaluateUni: func [ en ] [
for j 1 en 1[ st: copy ""
for i 1 en 1[
append st unitar i * j en
sr: square-root en
if ( unitar i * j en ) == 1  [ append positions ( as-pair i j  ) * 350 / en + 23x23 ]
]
]
positions
]
evaluateUni ena

refre: does[
positions: copy []
evaluateUni ena
pis: copy []
posi: copy positions
foreach p posi[ insert tail pis  reduce[ 'fill-pen 160.209.215.100 'circle p dimPal ]  ]
out: form ( length? positions ) / 2 == ( ena - 1 )
insert tail pis reduce [  'text 230x5 join "numero primo: "   out ]
scrn/effect/draw: copy []
append scrn/effect/draw pis
show scrn
]

refreNoEval: does[
pis: copy []
posi: copy positions
foreach p posi[ insert tail pis  reduce[ 'fill-pen 160.209.215.100 'circle p dimPal ]  ]
out: form ( length? positions ) / 2 == ( ena - 1 )
insert tail pis reduce [  'text 230x5 join "numero primo: "   out ]
scrn/effect/draw: copy []
append scrn/effect/draw pis
show scrn
]
lay: layout [

scrn: box 400x400 black effect [
draw [ text "unit" ]
rotate 50
gradmul 180.180.210 180.60.255
]
slider 200x16 ena / 300 [
ena: to-integer value * 300
inpNum/data: form ena
inpNum/text: form ena
show inpNum
refre
]
inpNum: field form ena [
print to-integer inpNum/text
ena: to-integer inpNum/text 
]
at 330x460
btn "Change"  [
refre
]
slider 100x15 dimPal / 10 [
dimPal: to-integer  value    * 10
refreNoEval
]
]

view lay