Lissajous Curves/Figures

[GeorgeMcGinn]

Hi Henk,

I love it. I see you have six types, but I was under the impression that there were an infinite number.

Is the infinite in the multi phases within each box since they change form?

Thanks.

graphics ! graphics clear .8,.8,.8
d=56 ! option angle degrees
fill color 1,1,1 ! refresh off
loop:
phaseX+=5 ! phaseY+=10
for i=0 to 2 ! for j=0 to 1
box(d+j*(300+d),20+i*320,300,300,.5,.5,15)
draw color 1,0,0 ! draw size 1
for a=0 to 720 step 2
x=9*sin((1+2*i)*a+phaseX) ! y=9*cos((1+1.5*j)*a+phaseY)
if a=0 then ! xo=x ! yo=y ! endif
draw_it(xo,yo,x,y) ! xo=x ! yo=y
next a
next j ! next i
refresh
goto loop

def box(xlu,ylu,width,height,xm,ym,scale)
org_x=xlu+xm*width ! org_y=ylu+(1-ym)*height
xrl=xlu+width ! yrl=ylu+height
draw size 4
draw color 0,0,0
fill rect xlu-4,ylu-4 to xrl+4,yrl+4
draw rect xlu-4,ylu-4 to xrl+4,yrl+4
draw size 1 ! draw alpha .2
step=scale
for x=org_x to xrl step step ! draw line x,ylu to x,yrl ! next x
for x=org_x to xlu step -step ! draw line x,ylu to x,yrl ! next x
for y=org_y to yrl step step ! draw line xlu,y to xrl,y ! next y
for y=org_y to ylu step -step ! draw line xlu,y to xrl,y ! next y
draw color 0,0,1 ! draw size 2 ! draw alpha 1
draw line xlu,org_y to xrl,org_y
draw line org_x,ylu to org_x,yrl
end def

def draw_it(xs,ys,xe,ye)
x1=box.org_x+box.scale*xs ! y1=box.org_y-box.scale*ys
x2=box.org_x+box.scale*xe ! y2=box.org_y-box.scale*ye
draw line x1,y1 to x2,y2
end def

[Henko]

Hi George,
The coefficients in X=ampl * sin ( omega * parameter + shift ) and Y = .....
are chosen in such a way that they produce 6 figures in ascending complexity. They change form due to the fact that the "shift" coefficients are modified a little bit in each loop.
I didn't know about Lissajoux "knots", interesting!

[GeorgeMcGinn]

I found the Knots interesting too. Let's see if we can code it.

Hi George,
...
I didn't know about Lissajoux "knots", interesting!

[GeorgeMcGinn]

Thanks - I will try this out.

I am having some success using the TRI which allows me to use the three parameters that LINE does not.

George.

Dr. Chip, is your code supposed to produce the color variations shown in your examples? I am only getting black and white images.

George, you won't get as realistic 3D shading as your rendered image, but you could still create get an impression of 3D.

When you draw the curves, start with black, increase it gradually to white for the first 1/3 of the iterations, stay white for the second third, and then gradually reduce intensity to black for the last 1/3. This will create a cylindrical look.