<content> <p> lookup(value,table,col) </p> </content>

ad2e5c76-4287-4cd5-9182-aa1871f07f97 5 4 5 false false 0 0 decimal

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

Any spiral [c,k,r] ...

value table col lookup k 1 : j k table rows range table j col el value ≡ index k el j : k k 1 + : 21 line continue if for k 1 ≡ index NO match : index if 31 line :

◄  The composite 'any' coefficients c 0.125 : k 0.125 : 12 mat

i (2^1 -

◄  The governing function x any c x * k + exp :

start 0 : end 5 π * : N 1000 : 13 mat u v N var u v u v u - N / + (range : x start end N var : 31 sys

± svg the spiral r 1.5 :

r x Ψ r e i x *^* (x any * i (2^* :

U r x Ψ Re vectorize :

V r x Ψ Im vectorize :

ANY U V augment eval :

Extremas Extr ANY 1 row ANY ANY rows row 21 sys : 1.6997 - 012 mat 12.0839 0.1898 - 12 mat 21 sys

ROW_1 ANY 2 col Max ANY 2 lookup : 70911 mat

ANY ROW_1 row 0.8554 - 6.7714 12 mat

ROW_2 ANY 1 col Min ANY 1 lookup : 80911 mat

ANY ROW_2 row 8.2404 - 1.041 - 12 mat

The spiral system ...
is fully automated wrt
the command line [c,k,r]
'r' is + in this demo.

ROW_3 ANY 2 col Min ANY 2 lookup : 90911 mat

ANY ROW_3 row 1.2669 10.0282 - 12 mat

data ANY ROW_1 row ANY ROW_2 row ANY ROW_3 row 31 sys : 0.855 - 6.771 12 mat 8.24 - 1.041 - 12 mat 1.267 10.028 - 12 mat 31 sys

plot ANY data 1 el 11 el data 1 el 12 el + 40 red 15 mat data 2 el 11 el data 2 el 12 el + 40 red 15 mat data 3 el 11 el data 3 el 12 el + 40 red 15 mat Extr 1 el 11 el Extr 1 el 12 el . 16 black 15 mat Extr 2 el 11 el Extr 2 el 12 el . 16 black 15 mat 61 sys :

t X U t el : t Y V t el : 12 mat

τ 1 U rows 5 range :

3 parameters command line spiral

plot t 1 ≡ path t X t Y 1 2 mat : path path t X t Y 1 2 mat stack : if Extr 2 el 1 1 el Extr 2 el 1 2 el . 16 black 1 5 mat 2 1 sys