Interesting non-random patterns discovered during my researches

[Mrwhy]

Walter, One of the weakest features of human knowledge is how we specialise.
We hide behind specialised jargon and IGNORE all other branches of knowledge.
This way you end up knowing all about nothing

On the other hand, one of the best and most rewarding sources of good ideas, inventions and discoveries is to APPLY knowledge learned in one field to a task that needs solving in another!

(For the "more graphics " you are asking for, see my 6 Coupled oscillators posted today)

[Clippy]

YOU CAN'T possibly be an EXPERT at everything! It is better to know ONE THING than to SPECIALIZE in knowing ABSOLUTELY NOTHING about EVERYTHING! You seem to do that marvelously...

[Mrwhy]

The wise man realises that the more he knows the more he becomes uncertain!

[DarthWho]

yes it is better to end up with crippling overspecialization than knowing nothing what so ever (you can at least do something); but then again it is better to be good at a lot of things than to cripple yourself by being overspecialized; then on top of that it is best to be a polymath and be good at everything and master several things.

[Clippy]

KIDS! NOBODY has EVER been good at EVERYTHING! But you can try or you can talk in PLATITUDES FOREVER and understand nothing!

[DarthWho]

good lord it is a figure of speech... how didn't you realize that

[OlDosLover]

Hi all,
   

KIDS! NOBODY has EVER been good at EVERYTHING! But you can try or you can talk in PLATITUDES FOREVER and understand nothing!

Good point and accurate. May i remind you that almosy every young boy is an EXPERT at ONE thing! Us older folk can only marvel at how good we use to be! (If you know what i mean).
OlDosLover.

[Mrwhy]

KIDS! NOBODY has EVER been good at EVERYTHING! But you can try or you can talk in PLATITUDES FOREVER and understand nothing!

 

[waltersmind]

MrWhy,

I played around with your second code sample a bit, and made some modifications. I wanted to see small sections of the graphics so I could get a better understanding of what was going on. Also, I took out the FOR...NEXT loop, the LABEL, the GOTO statement and made it where you can just press any key to exit the program. I got tired of using the Windows Task Manger to close the program.

After watching this version for a short bit, I starting thinking of all kids of creations I could make from this. I really would like to thank you again for sharing this fascinating graphical demo.

Code: [Select]

'@ 4 coupled oscillators
DEFDBL A-Z
_FULLSCREEN
SCREEN 12
WINDOW (-.5, -.5)-(.5, .5)

dt = .001
cd = .251
col = 1

x1o = cd: y1o = -cd
x2o = cd: y2o = cd
x3o = -cd: y3o = cd
x4o = -cd: y4o = -cd

x1 = x1o: x2 = x2o: x3 = x3o: x4 = x4o
y1 = y1o: y2 = y2o: y3 = y3o: y4 = y4o
x1 = x1 + .4: '***** try .04

v1y = .00012
'v1x = .00012 '***** try rem out this line

m1 = 2: m2 = 2: m3 = 2: m4 = 2

nsq = .0000001 '****try 00000012,11, 09,08 etc

n1sq = nsq: n2sq = nsq: n3sq = nsq: n4sq = nsq
n12sq = nsq: n13sq = nsq: n14sq = nsq
n23sq = nsq: n24sq = nsq
n34sq = nsq

ChangeColorDelay = 75000
ChangeColorMoment = 0

DO

    accn1x = -n1sq * (x1 - x1o) - n12sq * ((x1 - x2) - (x1o - x2o)) - n13sq * ((x1 - x3) - (x1o - x3o)) - n14sq * ((x1 - x4) - (x1o - x4o))
    accn1y = -n1sq * (y1 - y1o) - n12sq * ((y1 - y2) - (y1o - y2o)) - n13sq * ((y1 - y3) - (y1o - y3o)) - n14sq * ((y1 - y4) - (y1o - y4o))

    v1x = v1x + accn1x / m1
    v1y = v1y + accn1y / m1

    accn2x = -n2sq * (x2 - x2o) - n12sq * ((x2 - x1) - (x2o - x1o)) - n23sq * ((x2 - x3) - (x2o - x3o)) - n24sq * ((x2 - x4) - (x2o - x4o))
    accn2y = -n2sq * (y2 - y2o) - n12sq * ((y2 - y1) - (y2o - y1o)) - n23sq * ((y2 - y3) - (y2o - y3o)) - n24sq * ((y2 - y4) - (y2o - y4o))

    v2x = v2x + accn2x / m2
    v2y = v2y + accn2y / m2

    accn3x = -n3sq * (x3 - x3o) * (x3 - x3o) - n23sq * ((x3 - x2) - (x3o - x2o)) - n13sq * ((x3 - x1) - (x3o - x1o)) - n34sq * ((x3 - x4) - (x3o - x4o))
    accn3y = -n3sq * (y3 - y3o) * (y3 - y3o) - n23sq * ((y3 - y2) - (y3o - y2o)) - n13sq * ((y3 - y1) - (y3o - y1o)) - n34sq * ((y3 - y4) - (y3o - y4o))

    v3x = v3x + accn3x / m3
    v3y = v3y + accn3y / m3

    accn4x = -n4sq * (x4 - x4o) - n24sq * ((x4 - x2) - (x4o - x2o)) - n34sq * ((x4 - x3) - (x4o - x3o)) - n14sq * ((x4 - x1) - (x4o - x1o))
    accn4y = -n4sq * (y4 - y4o) - n24sq * ((y4 - y2) - (y4o - y2o)) - n34sq * ((y4 - y3) - (y4o - y3o)) - n14sq * ((y4 - y1) - (y4o - y1o))

    v4x = v4x + accn4x / m4
    v4y = v4y + accn4y / m4

    x1 = x1 + v1x
    y1 = y1 + v1y

    x2 = x2 + v2x
    y2 = y2 + v2y

    x3 = x3 + v3x
    y3 = y3 + v3y

    x4 = x4 + v4x
    y4 = y4 + v4y

    PSET (x1, y1), col
    PSET (x2, y2), col + 1
    PSET (x3, y3), col + 2
    PSET (x4, y4), col + 3

    ChangeColorMoment = (ChangeColorMoment + 1) MOD ChangeColorDelay

    IF ChangeColorMoment = 0 THEN
        _DISPLAY
        CLS
    END IF

    k$ = INKEY$: IF k$ <> "" THEN SYSTEM

LOOP



[Mrwhy]

Let me know what sort of things you'd like - glad to help if I can

[Mrwhy]

MrWhy,

I played around with your second code sample a bit, and made some modifications. I wanted to see small sections of the graphics so I could get a better understanding of what was going on.

I like  
Here is a more symmetical version

Can you get the orbits #2,#3,#4 stationary (with the "pointing arrows" touching)?

Code: [Select]

'@ 4 coupled oscillators
DEFDBL A-Z
_FULLSCREEN
SCREEN 12
WINDOW (-.5, -.5)-(.5, .5)

dt = .001
cd = .251
col = 1

x1o = cd: y1o = -cd
x2o = cd: y2o = cd
x3o = -cd: y3o = cd
x4o = -cd: y4o = -cd

x1 = x1o: x2 = x2o: x3 = x3o: x4 = x4o
y1 = y1o: y2 = y2o: y3 = y3o: y4 = y4o
x1 = x1 + .2: '***** try .04

v1y = .00009
'v1x = .00012 '***** try rem out this line

m1 = 2: m2 = 2: m3 = 2: m4 = 2

nsq = .00000006 '****try 00000012,11, 09,08 etc

n1sq = nsq: n2sq = nsq: n3sq = nsq: n4sq = nsq
n12sq = nsq: n13sq = nsq: n14sq = nsq
n23sq = nsq: n24sq = nsq
n34sq = nsq

ChangeColorDelay = 75000
ChangeColorMoment = 0

DO

    accn1x = -n1sq * (x1 - x1o) - n12sq * ((x1 - x2) - (x1o - x2o)) - n13sq * ((x1 - x3) - (x1o - x3o)) - n14sq * ((x1 - x4) - (x1o - x4o))
    accn1y = -n1sq * (y1 - y1o) - n12sq * ((y1 - y2) - (y1o - y2o)) - n13sq * ((y1 - y3) - (y1o - y3o)) - n14sq * ((y1 - y4) - (y1o - y4o))

    v1x = v1x + accn1x / m1
    v1y = v1y + accn1y / m1

    accn2x = -n2sq * (x2 - x2o) - n12sq * ((x2 - x1) - (x2o - x1o)) - n23sq * ((x2 - x3) - (x2o - x3o)) - n24sq * ((x2 - x4) - (x2o - x4o))
    accn2y = -n2sq * (y2 - y2o) - n12sq * ((y2 - y1) - (y2o - y1o)) - n23sq * ((y2 - y3) - (y2o - y3o)) - n24sq * ((y2 - y4) - (y2o - y4o))

    v2x = v2x + accn2x / m2
    v2y = v2y + accn2y / m2

    accn3x = -n3sq * (x3 - x3o) - n23sq * ((x3 - x2) - (x3o - x2o)) - n13sq * ((x3 - x1) - (x3o - x1o)) - n34sq * ((x3 - x4) - (x3o - x4o))
    accn3y = -n3sq * (y3 - y3o) - n23sq * ((y3 - y2) - (y3o - y2o)) - n13sq * ((y3 - y1) - (y3o - y1o)) - n34sq * ((y3 - y4) - (y3o - y4o))

    v3x = v3x + accn3x / m3
    v3y = v3y + accn3y / m3

    accn4x = -n4sq * (x4 - x4o) - n24sq * ((x4 - x2) - (x4o - x2o)) - n34sq * ((x4 - x3) - (x4o - x3o)) - n14sq * ((x4 - x1) - (x4o - x1o))
    accn4y = -n4sq * (y4 - y4o) - n24sq * ((y4 - y2) - (y4o - y2o)) - n34sq * ((y4 - y3) - (y4o - y3o)) - n14sq * ((y4 - y1) - (y4o - y1o))

    v4x = v4x + accn4x / m4
    v4y = v4y + accn4y / m4

    x1 = x1 + v1x
    y1 = y1 + v1y

    x2 = x2 + v2x
    y2 = y2 + v2y

    x3 = x3 + v3x
    y3 = y3 + v3y

    x4 = x4 + v4x
    y4 = y4 + v4y

    PSET (x1, y1), col
    PSET (x2, y2), col + 1
    PSET (x3, y3), col + 2
    PSET (x4, y4), col + 3

    ChangeColorMoment = (ChangeColorMoment + 1) MOD ChangeColorDelay

    IF ChangeColorMoment = 0 THEN
        _DISPLAY
        CLS
    END IF

    k$ = INKEY$: IF k$ <> "" THEN SYSTEM

LOOP



[Mrwhy]

Thios one?

Code: [Select]

'@ 4 coupled oscillators
DEFDBL A-Z
_FULLSCREEN
SCREEN 12
WINDOW (-.5, -.5)-(.5, .5)

dt = .001
cd = .251
col = 1

x1o = cd: y1o = -cd
x2o = cd: y2o = cd
x3o = -cd: y3o = cd
x4o = -cd: y4o = -cd

x1 = x1o: x2 = x2o: x3 = x3o: x4 = x4o
y1 = y1o: y2 = y2o: y3 = y3o: y4 = y4o
x1 = x1 + .2: '***** try .04
x3 = x3 - .2

x2 = x2 + .1
x4 = x4 - .1
v1y = .000023
v3y = .000023
v2y = .000023
v4y = .000023
'v1x = .00012 '***** try rem out this line

m1 = 1: m2 = 1.01: m3 = 1.02: m4 = 1.03

nsq = .0000000125 '****try 00000012,11, 09,08 etc

n1sq = nsq: n2sq = nsq: n3sq = nsq: n4sq = nsq
n = nsq / 25
n12sq = n: n13sq = n: n14sq = n
n23sq = n: n24 = n
n34sq = n

ChangeColorDelay = 475000
ChangeColorMoment = 0

DO

    accn1x = -n1sq * (x1 - x1o) - n12sq * ((x1 - x2) - (x1o - x2o)) - n13sq * ((x1 - x3) - (x1o - x3o)) - n14sq * ((x1 - x4) - (x1o - x4o))
    accn1y = -n1sq * (y1 - y1o) - n12sq * ((y1 - y2) - (y1o - y2o)) - n13sq * ((y1 - y3) - (y1o - y3o)) - n14sq * ((y1 - y4) - (y1o - y4o))

    v1x = v1x + accn1x / m1
    v1y = v1y + accn1y / m1

    accn2x = -n2sq * (x2 - x2o) - n12sq * ((x2 - x1) - (x2o - x1o)) - n23sq * ((x2 - x3) - (x2o - x3o)) - n24sq * ((x2 - x4) - (x2o - x4o))
    accn2y = -n2sq * (y2 - y2o) - n12sq * ((y2 - y1) - (y2o - y1o)) - n23sq * ((y2 - y3) - (y2o - y3o)) - n24sq * ((y2 - y4) - (y2o - y4o))

    v2x = v2x + accn2x / m2
    v2y = v2y + accn2y / m2

    accn3x = -n3sq * (x3 - x3o) - n23sq * ((x3 - x2) - (x3o - x2o)) - n13sq * ((x3 - x1) - (x3o - x1o)) - n34sq * ((x3 - x4) - (x3o - x4o))
    accn3y = -n3sq * (y3 - y3o) - n23sq * ((y3 - y2) - (y3o - y2o)) - n13sq * ((y3 - y1) - (y3o - y1o)) - n34sq * ((y3 - y4) - (y3o - y4o))

    v3x = v3x + accn3x / m3
    v3y = v3y + accn3y / m3

    accn4x = -n4sq * (x4 - x4o) - n24sq * ((x4 - x2) - (x4o - x2o)) - n34sq * ((x4 - x3) - (x4o - x3o)) - n14sq * ((x4 - x1) - (x4o - x1o))
    accn4y = -n4sq * (y4 - y4o) - n24sq * ((y4 - y2) - (y4o - y2o)) - n34sq * ((y4 - y3) - (y4o - y3o)) - n14sq * ((y4 - y1) - (y4o - y1o))

    v4x = v4x + accn4x / m4
    v4y = v4y + accn4y / m4

    x1 = x1 + v1x
    y1 = y1 + v1y

    x2 = x2 + v2x
    y2 = y2 + v2y

    x3 = x3 + v3x
    y3 = y3 + v3y

    x4 = x4 + v4x
    y4 = y4 + v4y

    PSET (x1, y1), col
    PSET (x2, y2), col + 1
    PSET (x3, y3), col + 2
    PSET (x4, y4), col + 3

    ChangeColorMoment = (ChangeColorMoment + 1) MOD ChangeColorDelay

    IF ChangeColorMoment = 0 THEN
        _DISPLAY
        col = col + 1
        'CLS
    END IF

    k$ = INKEY$: IF k$ <> "" THEN SYSTEM

LOOP



[Mrwhy]

A variant 6

Code: [Select]

'@ 6 coupled oscillators
DEFDBL A-Z
_FULLSCREEN
SCREEN 12
WINDOW (-.5, -.5)-(.5, .5)

dt = .001
cd = .251
col = 1

x1o = cd: y1o = -cd
x2o = cd: y2o = cd
x3o = -cd: y3o = cd
x4o = -cd: y4o = -cd
x5o = 0: y5o = cd
x6o = 0: y6o = -cd
x1 = x1o: x2 = x2o: x3 = x3o: x4 = x4o
y1 = y1o: y2 = y2o: y3 = y3o: y4 = y4o
x5 = x5o: x6 = x6o
y5 = y5o: y6 = y6o


x1 = x1 + .2: '***** try .04
'x3 = x3 - .2

'x2 = x2 + .1
'x4 = x4 - .1
v1y = .00003
'v3y = .000023
'v2y = .000023
'v4y = .000023
'v1x = .00012 '***** try rem out this line

m1 = 1: m2 = 1.01: m3 = 1.02: m4 = 1.03: m5 = 1.04: m6 = 1.05

nsq = .0000000125 '****try 00000012,11, 09,08 etc

n1sq = nsq: n2sq = nsq: n3sq = nsq: n4sq = nsq: n5sq = nsq: n6sq = nsq
n = nsq / 25
n12sq = n: n13sq = n: n14sq = n: n15sq = n: n16sq = n
n23sq = n: n24 = n: n25sq = n: n26sq = n
n34sq = n: n35 = n: n36sq = n
n45sq = n: n46sq = n
n56sq = n

ChangeColorDelay = 875000
ChangeColorMoment = 0

DO

    accn1x = -n1sq * (x1 - x1o) - n12sq * ((x1 - x2) - (x1o - x2o)) - n13sq * ((x1 - x3) - (x1o - x3o))
    accn1x = accn1x - n14sq * ((x1 - x4) - (x1o - x4o)) - n15sq * ((x1 - x5) - (x1o - x5o)) - n16sq * ((x1 - x6) - (x1o - x6o))
    accn1y = -n1sq * (y1 - y1o) - n12sq * ((y1 - y2) - (y1o - y2o)) - n13sq * ((y1 - y3) - (y1o - y3o))
    accn1y = accn1y - n14sq * ((y1 - y4) - (y1o - y4o)) - n15sq * ((y1 - y5) - (y1o - y5o)) - n16sq * ((y1 - y6) - (y1o - y6o))

    v1x = v1x + accn1x / m1
    v1y = v1y + accn1y / m1

    accn2x = -n2sq * (x2 - x2o) - n12sq * ((x2 - x1) - (x2o - x1o)) - n23sq * ((x2 - x3) - (x2o - x3o))
    accn2x = accn2x - n24sq * ((x2 - x4) - (x2o - x4o)) - n25sq * ((x2 - x5) - (x2o - x5o)) - n26sq * ((x2 - x6) - (x2o - x6o))
    accn2y = -n2sq * (y2 - y2o) - n12sq * ((y2 - y1) - (y2o - y1o)) - n23sq * ((y2 - y3) - (y2o - y3o))
    accn2y = accn2y - n24sq * ((y2 - y4) - (y2o - y4o)) - n25sq * ((y2 - y5) - (y2o - y5o)) - n26sq * ((y2 - y6) - (y2o - y6o))
    v2x = v2x + accn2x / m2
    v2y = v2y + accn2y / m2

    accn3x = -n3sq * (x3 - x3o) - n23sq * ((x3 - x2) - (x3o - x2o)) - n13sq * ((x3 - x1) - (x3o - x1o))
    accn3x = accn3x - n34sq * ((x3 - x4) - (x3o - x4o)) - n35sq * ((x3 - x5) - (x3o - x5o)) - n36sq * ((x3 - x6) - (x3o - x6o))
    accn3y = -n3sq * (y3 - y3o) - n23sq * ((y3 - y2) - (y3o - y2o)) - n13sq * ((y3 - y1) - (y3o - y1o))
    accn3y = accn3y - n34sq * ((y3 - y4) - (y3o - y4o)) - n35sq * ((y3 - y5) - (y3o - y5o)) - n36sq * ((y3 - y6) - (y3o - y6o))
    v3x = v3x + accn3x / m3
    v3y = v3y + accn3y / m3

    accn4x = -n4sq * (x4 - x4o) - n24sq * ((x4 - x2) - (x4o - x2o)) - n34sq * ((x4 - x3) - (x4o - x3o))
    accn4x = accn4x - n14sq * ((x4 - x1) - (x4o - x1o)) - n45sq * ((x4 - x5) - (x4o - x5o)) - n46sq * ((x4 - x6) - (x4o - x6o))
    accn4y = -n4sq * (y4 - y4o) - n24sq * ((y4 - y2) - (y4o - y2o)) - n34sq * ((y4 - y3) - (y4o - y3o))
    accn4y = accn4y - n14sq * ((y4 - y1) - (y4o - y1o)) - n45sq * ((y4 - y5) - (y4o - y5o)) - n46sq * ((y4 - y6) - (y4o - y6o))

    v4x = v4x + accn4x / m4
    v4y = v4y + accn4y / m4

    accn5x = -n5sq * (x5 - x5o) - n25sq * ((x5 - x2) - (x5o - x2o)) - n35sq * ((x5 - x3) - (x5o - x3o))
    accn5x = accn5x - n15sq * ((x5 - x1) - (x5o - x1o)) - n45sq * ((x5 - x4) - (x5o - x4o)) - n46sq * ((x6 - x4) - (x6o - x4o))
    accn5y = -n5sq * (y5 - y5o) - n24sq * ((y5 - y2) - (y5o - y2o)) - n35sq * ((y5 - y3) - (y5o - y3o))
    accn5y = accn5y - n15sq * ((y5 - y1) - (y5o - y1o)) - n45sq * ((y5 - y4) - (y5o - y4o)) - n56sq * ((y5 - y6) - (y5o - y6o))
    v5x = v5x + accn5x / m5
    v5y = v5y + accn5y / m5

    accn6x = -n6sq * (x6 - x6o) - n26sq * ((x6 - x2) - (x6o - x2o)) - n36sq * ((x6 - x3) - (x6o - x3o))
    accn6x = accn6x - n16sq * ((x6 - x1) - (x6o - x1o)) - n46sq * ((x6 - x4) - (x6o - x4o)) - n56sq * ((x6 - x5) - (x6o - x5o))
    accn6y = -n6sq * (y6 - y6o) - n26sq * ((y6 - y2) - (y6o - y2o)) - n36sq * ((y6 - y3) - (y6o - y3o))
    accn6y = accn6y - n16sq * ((y6 - y1) - (y6o - y1o)) - n46sq * ((y6 - y4) - (y6o - y4o)) - n56sq * ((y6 - y5) - (y6o - y5o))
    v6x = v6x + accn6x / m6
    v6y = v6y + accn6y / m6

    x1 = x1 + v1x
    y1 = y1 + v1y

    x2 = x2 + v2x
    y2 = y2 + v2y

    x3 = x3 + v3x
    y3 = y3 + v3y

    x4 = x4 + v4x
    y4 = y4 + v4y

    x5 = x5 + v5x
    y5 = y5 + v5y

    x6 = x6 + v6x
    y6 = y6 + v6y

    PSET (x1, y1), col
    PSET (x2, y2), col + 1
    PSET (x3, y3), col + 2
    PSET (x4, y4), col + 3
    PSET (x5, y5), col + 4
    PSET (x6, y6), col + 5

    ChangeColorMoment = (ChangeColorMoment + 1) MOD ChangeColorDelay

    IF ChangeColorMoment = 0 THEN
        _DISPLAY
        col = col + 1
        CLS
    END IF

    k$ = INKEY$: IF k$ <> "" THEN SYSTEM

LOOP



[waltersmind]

MrWhy,

Since I am taking a lunch break at this moment, I wanted to read a little in the forums. I love the last three samples. I will look at your challenge a little later, but I wanted to send this modification to you. It is a slight modification to you last "Variant 6 - 6 coupled oscillators" demo. I REMed out the CLS and _DISPLAY commands and changed the color variable (col). I am trying to visualize the results a little different.

Code: [Select]

'@ 6 coupled oscillators
DEFDBL A-Z
_FULLSCREEN
SCREEN 12
WINDOW (-.5, -.5)-(.5, .5)

dt = .001
cd = .251
col = 1

x1o = cd: y1o = -cd
x2o = cd: y2o = cd
x3o = -cd: y3o = cd
x4o = -cd: y4o = -cd
x5o = 0: y5o = cd
x6o = 0: y6o = -cd
x1 = x1o: x2 = x2o: x3 = x3o: x4 = x4o
y1 = y1o: y2 = y2o: y3 = y3o: y4 = y4o
x5 = x5o: x6 = x6o
y5 = y5o: y6 = y6o


x1 = x1 + .2: '***** try .04
'x3 = x3 - .2

'x2 = x2 + .1
'x4 = x4 - .1
v1y = .00003
'v3y = .000023
'v2y = .000023
'v4y = .000023
'v1x = .00012 '***** try rem out this line

m1 = 1: m2 = 1.01: m3 = 1.02: m4 = 1.03: m5 = 1.04: m6 = 1.05

nsq = .0000000125 '****try 00000012,11, 09,08 etc

n1sq = nsq: n2sq = nsq: n3sq = nsq: n4sq = nsq: n5sq = nsq: n6sq = nsq
n = nsq / 25
n12sq = n: n13sq = n: n14sq = n: n15sq = n: n16sq = n
n23sq = n: n24 = n: n25sq = n: n26sq = n
n34sq = n: n35 = n: n36sq = n
n45sq = n: n46sq = n
n56sq = n

ChangeColorDelay = 875000
ChangeColorMoment = 0

DO

    accn1x = -n1sq * (x1 - x1o) - n12sq * ((x1 - x2) - (x1o - x2o)) - n13sq * ((x1 - x3) - (x1o - x3o))
    accn1x = accn1x - n14sq * ((x1 - x4) - (x1o - x4o)) - n15sq * ((x1 - x5) - (x1o - x5o)) - n16sq * ((x1 - x6) - (x1o - x6o))
    accn1y = -n1sq * (y1 - y1o) - n12sq * ((y1 - y2) - (y1o - y2o)) - n13sq * ((y1 - y3) - (y1o - y3o))
    accn1y = accn1y - n14sq * ((y1 - y4) - (y1o - y4o)) - n15sq * ((y1 - y5) - (y1o - y5o)) - n16sq * ((y1 - y6) - (y1o - y6o))

    v1x = v1x + accn1x / m1
    v1y = v1y + accn1y / m1

    accn2x = -n2sq * (x2 - x2o) - n12sq * ((x2 - x1) - (x2o - x1o)) - n23sq * ((x2 - x3) - (x2o - x3o))
    accn2x = accn2x - n24sq * ((x2 - x4) - (x2o - x4o)) - n25sq * ((x2 - x5) - (x2o - x5o)) - n26sq * ((x2 - x6) - (x2o - x6o))
    accn2y = -n2sq * (y2 - y2o) - n12sq * ((y2 - y1) - (y2o - y1o)) - n23sq * ((y2 - y3) - (y2o - y3o))
    accn2y = accn2y - n24sq * ((y2 - y4) - (y2o - y4o)) - n25sq * ((y2 - y5) - (y2o - y5o)) - n26sq * ((y2 - y6) - (y2o - y6o))
    v2x = v2x + accn2x / m2
    v2y = v2y + accn2y / m2

    accn3x = -n3sq * (x3 - x3o) - n23sq * ((x3 - x2) - (x3o - x2o)) - n13sq * ((x3 - x1) - (x3o - x1o))
    accn3x = accn3x - n34sq * ((x3 - x4) - (x3o - x4o)) - n35sq * ((x3 - x5) - (x3o - x5o)) - n36sq * ((x3 - x6) - (x3o - x6o))
    accn3y = -n3sq * (y3 - y3o) - n23sq * ((y3 - y2) - (y3o - y2o)) - n13sq * ((y3 - y1) - (y3o - y1o))
    accn3y = accn3y - n34sq * ((y3 - y4) - (y3o - y4o)) - n35sq * ((y3 - y5) - (y3o - y5o)) - n36sq * ((y3 - y6) - (y3o - y6o))
    v3x = v3x + accn3x / m3
    v3y = v3y + accn3y / m3

    accn4x = -n4sq * (x4 - x4o) - n24sq * ((x4 - x2) - (x4o - x2o)) - n34sq * ((x4 - x3) - (x4o - x3o))
    accn4x = accn4x - n14sq * ((x4 - x1) - (x4o - x1o)) - n45sq * ((x4 - x5) - (x4o - x5o)) - n46sq * ((x4 - x6) - (x4o - x6o))
    accn4y = -n4sq * (y4 - y4o) - n24sq * ((y4 - y2) - (y4o - y2o)) - n34sq * ((y4 - y3) - (y4o - y3o))
    accn4y = accn4y - n14sq * ((y4 - y1) - (y4o - y1o)) - n45sq * ((y4 - y5) - (y4o - y5o)) - n46sq * ((y4 - y6) - (y4o - y6o))

    v4x = v4x + accn4x / m4
    v4y = v4y + accn4y / m4

    accn5x = -n5sq * (x5 - x5o) - n25sq * ((x5 - x2) - (x5o - x2o)) - n35sq * ((x5 - x3) - (x5o - x3o))
    accn5x = accn5x - n15sq * ((x5 - x1) - (x5o - x1o)) - n45sq * ((x5 - x4) - (x5o - x4o)) - n46sq * ((x6 - x4) - (x6o - x4o))
    accn5y = -n5sq * (y5 - y5o) - n24sq * ((y5 - y2) - (y5o - y2o)) - n35sq * ((y5 - y3) - (y5o - y3o))
    accn5y = accn5y - n15sq * ((y5 - y1) - (y5o - y1o)) - n45sq * ((y5 - y4) - (y5o - y4o)) - n56sq * ((y5 - y6) - (y5o - y6o))
    v5x = v5x + accn5x / m5
    v5y = v5y + accn5y / m5

    accn6x = -n6sq * (x6 - x6o) - n26sq * ((x6 - x2) - (x6o - x2o)) - n36sq * ((x6 - x3) - (x6o - x3o))
    accn6x = accn6x - n16sq * ((x6 - x1) - (x6o - x1o)) - n46sq * ((x6 - x4) - (x6o - x4o)) - n56sq * ((x6 - x5) - (x6o - x5o))
    accn6y = -n6sq * (y6 - y6o) - n26sq * ((y6 - y2) - (y6o - y2o)) - n36sq * ((y6 - y3) - (y6o - y3o))
    accn6y = accn6y - n16sq * ((y6 - y1) - (y6o - y1o)) - n46sq * ((y6 - y4) - (y6o - y4o)) - n56sq * ((y6 - y5) - (y6o - y5o))
    v6x = v6x + accn6x / m6
    v6y = v6y + accn6y / m6

    x1 = x1 + v1x
    y1 = y1 + v1y

    x2 = x2 + v2x
    y2 = y2 + v2y

    x3 = x3 + v3x
    y3 = y3 + v3y

    x4 = x4 + v4x
    y4 = y4 + v4y

    x5 = x5 + v5x
    y5 = y5 + v5y

    x6 = x6 + v6x
    y6 = y6 + v6y

    PSET (x1, y1), col
    PSET (x2, y2), col + 1
    PSET (x3, y3), col + 2
    PSET (x4, y4), col + 3
    PSET (x5, y5), col + 4
    PSET (x6, y6), col + 5

    ChangeColorMoment = (ChangeColorMoment + 1) MOD ChangeColorDelay

    IF ChangeColorMoment = 0 THEN
        '_DISPLAY
        col = ((col + 1) MOD 10) + 1
        'CLS
    END IF

    k$ = INKEY$: IF k$ <> "" THEN SYSTEM

LOOP


[Mrwhy]

Walter, I am so glad you are having fun - I spent hours trying to get colours like that!

At one stage I had #1 and #2 out of phase (push-pull) and '"top left" going steady at TWICE the frequency of the waxing and waning of #1 and #2

In THEORY we should be able to get "resonance" between the frequency each # bounces among its NEIGHBOURS and the frequency at which #1 DRIVES it (prods it)

Resonance usually gives huge amplitude motion but if the resonance is at 2f, 3f etc it will amplify only the small harmonics of the motion of #1
And here there is also FEEDBACk (to #1) as to what #2,#3,#4,#5  and #6 are doing

An interesting idea to try is DELAYED feedback
A chap called Nyquist made himself famous thinking about feedback delay-times in amplifiers.
A chap called Black made the FIRST GOOD amplifiers using NEGATIVE feedback. Everyone ridiculed him for the way to get GAIN (amplification) is to use POSITIVE feedback (self-oscillating devices, lasers, feedbock auditorioum howl)