<p> plotG(vx,vy,a,b,c) </p>

14e450a8-7a88-4ca4-9084-9a89214685ec 5 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

Fibonacci recursive sequence

If the Bolean condition inside "while" is not true => endless loop => PROBLEM ! --------- Thanks Smath tutor ---------

n 18 :

<----------- end of the counter

fib 1 el 1 :

fib 2 el 1 :

<= initialise the two first fib.

i 3 :

<----------- start of the counter

i n ≤ fib i el fib i 1 - el fib i 2 - el + : i i 1 + : 21 line while

fib transpose 112358132134558914423337761098715972584118 mat

N Fib Fib 2 el 1 : Fib 3 el 1 : 12 mat i 3 : i N ≤ Fib i el Fib i 1 - el Fib i 2 - el + : i i 1 + : 21 line while Fib 41 line :

21 Fib transpose 011235813213455891442333776109871597258441816765121 mat

n V i 0 : i n ≤ p i 1 + el i 3^: i i 1 + : 21 line while p 31 line :

8 V 018276412521634351291 mat

14 Fib transpose 01123581321345589144233114 mat

x f x 1 x / sin * :

V v 1 el 0 : i 1 : i 10 / f 0.75 ≤ v i 1 + el i 10 / f : i i 1 + : 21 line while v 41 line :

V 0 0.054402 - 0.191785 - 0.05717 - 0.239389 0.454649 0.597245 0.692932 81 mat

Unform ...  -1 < rnd < 1 n rnd μ n : 2 μ Random * 1 - 21 line :

collect next above hitrnd i 0 : x 0 : x 0.5 ≤ x 1 rnd 1 el abs : v i 1 + el x : i i 1 + : 31 line while v 41 line :

hitrnd sort 0.806 11 mat

v 0 :

x 0 :

collect next below value hitrnd i 0 : x 0 : x value ≤ x 1 rnd 1 el abs : v i 1 + el x : i i 1 + : 31 line while i 1 v rows 1 - range u i el v i el : for u 21 line 41 line :

hitrnd sort 0.982 11 mat

v 0 :

x 0 :

collect next below hitrnd i 0 : x 1 rnd 1 el abs : x 0.75 ≤ v i 1 + el x : i i 1 + : x 1 rnd 1 el abs : 41 line while v 41 line :

hitrnd sort 0.103 11 mat

x y GCD x 0 ≡ x y GCD y : y x mod x GCD if :

94590 GCD 945

n fact fact 1 el 1 : fact 2 el 1 : i 2 : i n ≤ fact i el i 1 - (fact i 1 - el * : i i 1 + : 21 line while fact 21 line 41 line :

7 fact 11262412072071 mat

Fibonacci on-line n Fib 15 sqrt + (n^15 sqrt - (n^- 5 sqrt 2 n^* / :

7 Fib 13

Tom G. Fibonacci incremental algorithm λ Fibonnacci Fib 0 : i 1 λ range Fib i el 15 sqrt + (i^15 sqrt - (i^- 5 sqrt 2 i^* / : idx i el i : 21 line for idx Fib augment 31 line :

λ 16 :

vx λ Fibonnacci 1 col : vy λ Fibonnacci 2 col : XY vx vy . 13 red plotG : 31 line

21 Fibonnacci 1121324355687 13.0000000000001 82193410 55.0000000000001 11 88.9999999999998 12 144.000000000001 1323314 377.000000000003 1561016 986.999999999999 17 1.597 103^* 18 2.584 103^* 19 4.18100000000001 103^* 20 6.76500000000001 103^* 21 1.09460000000001 104^* 212 mat

λ Fibonnacci XY 2 1 sys

Tom G. Fibonacci incremental algorithm λ Fibonnacci Fib 0 : i 1 λ range Fib i el 15 sqrt + (i^15 sqrt - (i^- 5 sqrt 2 i^* / : idx i el i : 21 line for idx Fib 0 round vectorize augment 31 line :

11 Fibonnacci transpose 12345678910111123581321345589211 mat

Fibonnacci incremental algorithm λ Fib set Exponential threshold data n 1 + el MCD ORIGIN 0 ≡ 21 sys n 1 λ range Fib n 1 + el 15 sqrt + 2 / (n^15 sqrt - 2 / (n^- (5 sqrt 5 / * : idx n 1 + el n : 21 line for idx Fib 0 round vectorize augment 31 line :

15 sqrt + 2 / (n^15 sqrt - 2 / (n^- (5 sqrt 5 / * 15 sqrt + (n^15 sqrt - (n^- 5 sqrt 2 n^* / ≡

21 Fib transpose 012345678910111213141516171819202101123581321345589144233377610987159725844181676510946222 mat

a 0.894839 - : b 1.790649 : c 0.104191 : d 0.06125 : 41 sys

0.894839 - 1.790649 0.104191 0.417733 41 mat

Recursive Process Control Instrumentation

user u 5 :

up dn locate vert j 1 up range v j el j dn + : u j el locate j 0 * + : 21 line for u v augment 21 line :

X j 160 range X j el j u / : for X 21 line :

f s 1 el 0 : s 2 el 1 : n 360 range s n el a s n 2 - el * b s n 1 - el * + c X n 2 - el * + d + : for i 1 s rows range x i el i : for x s augment 31 line 31 line :

Vert 305 - 60 vert :

x u / f X X rows el Vert 4 1 sys

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

Recursive behaviour 2nd order system

a 0.894839 - : b 1.790648 : c 0.104191 : 31 sys

a b + c + 1

SetPoint SP 1 :

Shrink/Expand ε 0.75 :

Title 2 0.375 - response 2nd order under SetPoint 11 black 15 mat :

UnitSP s 1 el 0 : s 2 el 0 : n 3100 range s n el a s n 2 - el * b s n 1 - el * + c SP * + : for i 1 s rows range x i el i : for x ε * s augment 51 line :

a b c spec . 8 blue 13 mat : Pts UnitSP a b c spec pts : 21 sys

Pts SP Title 3 1 sys