Liassajou curves are described by the parametric equations below:spherical Lissajous curves can be. Lissajous curves (sometimes also known as Lissajous figures or Bowditch curves), are pretty shapes first investigated by Nathaniel Bowditch in 1815, and later (and in much more detail) by Jules Antoine Lissajou in 1857. This is an article about Lissajous Curves.

The goal for this project was to create an interactive and reactive visualiser for an 808-like drum sequencer. 311-325.A Lissajous figure, made by releasing sand from a container at the end of a BlackburnвЂ…pendulumOscilloscope Drum Machine. Generator, Computers and Biomedical Research 17.

For a ratio of 1, the figure is an ellipse, with special cases including circles ( A = B, Оґ = ПЂ / 2 radians) and lines ( Оґ = 0). This family of curves was investigated by NathanielвЂ…Bowditch in 1815, and later in more detail in 1857 by JulesвЂ…AntoineвЂ…Lissajous (for whom it has been named).The appearance of the figure is highly sensitive to the ratio a / b. Other one to the secondary coil of the transformer of a power generator (a V-20 Corona.A Lissajous curve / Л€ l ЙЄ s Й™ К’ uЛђ/, also known as Lissajous figure or Bowditch curve / Л€ b aКЉ d ЙЄ tКѓ/, is the graph of a system of parametricвЂ…equations x = A sin вЃЎ ( a t + Оґ ) , y = B sin вЃЎ ( b t ) , Which describe complexвЂ…harmonicвЂ…motion. These patterns are called 'Lissajous' patterns (Ive included some gifs of these).Lissajous figures, obtained by means of a high-voltage and a.

Similarly, a ratio of 5 / 4 produces a figure with five horizontal lobes and four vertical lobes. For example, a ratio of 3 / 1 or 1 / 3 produces a figure with three major lobes (see image). The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as LissajousвЂ…knots, project to the plane as Lissajous figures.Visually, the ratio a / b determines the number of 'lobes' of the figure. Other ratios produce more complicated curves, which are closed only if a / b is rational.

Finally, the value of Оґ determines the apparent 'rotation' angle of the figure, viewed as if it were actually a three-dimensional curve. For example, a ratio of 2 / 1 produces a figure that is twice as wide as it is high. The ratio A / B determines the relative width-to-height ratio of the curve.

The arrows show the direction of rotation of the Lissajous figure. The phase shifts are all negative so that delay semantics can be used with a causal LTI system (note that в€’270В° is equivalent to +90В°). The figure below summarizes how the Lissajous figure changes over different phase shifts. The aspectвЂ…ratio of the resulting ellipse is a function of the phase shift between the input and output, with an aspect ratio of 1 (perfect circle) corresponding to a phase shift of в™0В° and an aspect ratio of в€ћ (a line) corresponding to a phase shift of 0В° or 180В°. Using an oscilloscope that can plot one signal against another (as opposed to one signal against time) to plot the output of an LTI system against the input to the LTI system produces an ellipse that is a Lissajous figure for the special case of a = b. In this particular example, because the output is 90 degrees out of phase from the input, the Lissajous curve is a circle, and is rotating counterclockwise.When the input to an LTIвЂ…system is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some phaseвЂ…shift.

Lissajous Pattern Generator