Manuals/calci/LISSAJOUS

LISSAJOUS (TypeOrSettings,AsTable)

• $TypeOrSettings$ is any type like Ellipse or circle and so on.

Description

• This function shows the values of the Lissajous curve.
• Lissajous Curve is a parametric plot of the harmonic system.
• It is also called Bowditch Curves.
• Lissajous used sounds of different frequencies to vibrate a mirror.
• A beam of light reflected from the mirror, was allowed to trace patterns which depended on the frequencies of the sounds – in a setup similar to projectors used in today's laser light shows.Lissajous figure is the intersection of two sinusoidal curves, the axes of which are at right angles to each other.
• Mathematically, this translates to a Complex harmonic function: In the Lissajous equation,a=1,b=1,A=1,B=1 and $\delta$ = ${\frac {\pi }{2}}$ radians, the figure is a circle.
• So these values substitute in the equation and it will shows the result.With the above values when $\delta$=0,then the value will show for line.
• In the same way the ratio ${\frac {a}{b}}$=1 and $\delta$=0,then the values will be shown for ellipse.
• Suppose ${\frac {a}{b}}$ = 2, $\delta$ = ${\frac {\pi }{4}}$, then the values will show for parabola.
• The Lissajous curve gets more complicated for other ratios, which are closed only if a/b is rational.

Examples

1. LISSAJOUS("circle",4..6)

4.999998731727338	1
4.98033339924072	1.3993336665873126
4.9208978911521815	1.7946773231802449
4.822286067411776	2.1820808266453584
4.685483224765582	2.5576733692346023
4.511856251996312	2.917702154416812
4.303139972422432	3.2585698935801415
4.061419810117014	3.576870748950764
3.789110953039751	3.8694243635980907
3.48893422127722	4.133307638509933
3.163888881507954	4.365883939231585
2.817222679321226	4.564829440245742
2.4523993888166733	4.728156343868905
2.073064203718472	4.854232741668772

and so on.

Related Videos

Lissajous

See Also

• MANDELBROT
• FRACTAL
• LISSAJOUSCURVE

References

• Lissajous

• List of Main Z Functions

• Z3 home