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.

See Also

• MANDELBROT
• FRACTAL
• LISSAJOUSCURVE

References

• Lissajous

• List of Main Z Functions

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