Circles System

afc63ca8-47d3-40c6-a4c5-d3b229a3523a 15 9 12 decimal

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Circles System

tt rkf D A rkf 1 el rkf 2 el 21 mat * :

A 022 - 022 mat :

N 200 : span 1 N π * / : α π : (overlap ≡ 31 line

tt rkf D 022 - 022 mat rkf 1 el rkf 2 el 21 mat *

Circles U 00013 mat : p 0.375 0.75 113 mat W p span 21 mat : Urk W 0 α N tt rkf D rkfixed : U U Urk stack : 31 line for B U 3 col U 2 col augment : 31 line :

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radius circle
-------- Y0 0 1.25 031 mat :

t0 0 : t1 2 π * : N 12 : 31 line

Radial plot is essentially built from Rkadapt suject to user parameters [radius,t0,t1,N]

Radial Construction

Rename: Y => .. else variable name t u RK u 2 el u 3 el 1 u 1 el (2^- (* u 2 el * (u 1 el - 031 mat :

Either 'rkfixed' or 'Rkadapt' s Y0 t0 t1 N t u RK Rkadapt :

X s 2 col : Y s 3 col : SOL X Y augment : 31 line

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem N vy length : i 1 N range q i el 3 : q N el 2 : 21 line for 11 line i 1 N range v i el i : for i 1 N range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

SOL X Y augment : radial SOL 1 col stem 2 col SOL 2 col stem 2 col augment : 21 sys

spiral 0 π - 4 / + rot * spiral π 2 / π - 4 / + rot * spiral π π - 4 / + rot * spiral 3 π * 2 / π - 4 / + rot * x C1 x C2 x C3 radial 81 sys

θ rot θ cos θ sin - θ sin θ cos 22 mat :

start 4 π * - : end 4 π * : N 500 : 13 mat u v N var u v u v u - N / + (range : xf start end N var : 31 sys

Circle ± definition a x C a 2^x 2^- sqrt ± :

xf X xf cos xf exp * : xf Y xf sin xf exp * : spiral xf X vectorize xf Y vectorize augment : 31 sys

x C1 1 x C : x C2 0.75 x C : x C3 0.375 x C : 31 sys

Imitates Mathcad: 4 flies chasing each other

User circles over radial mesh

1 x C 0.75 x C 0.375 x C radial 4 1 sys spiral 0 π - 4 / + rot * spiral π 2 / π - 4 / + rot * spiral π π - 4 / + rot * spiral 3 π * 2 / π - 4 / + rot * x C1 x C2 x C3 radial 8 1 sys spiral 0 π - 4 / + rot * spiral π 2 / π - 4 / + rot * spiral π π - 4 / + rot * spiral 3 π * 2 / π - 4 / + rot * radial Circles 6 1 sys