Polar Curves

- XLogo


All these curves are generated using equations in polar (Radius and Theta) form.

Usually, we plot points using X Y co-ordinates, (or Rectangular notation). A pair of numbers, define the horizontal and vertical distance from the origin. In XLogo, the command SetXY moves the turtle to any XY point on the screen.

Alternatively, we can use polar co-ordinates. These again use a pair of numbers. The first (called Radius) gives the distance from the origin. The second (called Theta) gives the angle or bearing (measured from North).

Again, we can move the turtle to any point on the screen.
Note that using polar notation, points can be expressed in more than one way. We can turn in a positive or negative direction. Also the Radius can be positive (forward) or negative (back).

Sometimes, they are then converted into X Y co-ordinates for drawing by the turtle using the SetXY command by the procedure P2R (polar to rectangular). It requires two varibles, Radius and Theta and outputs the X and Y co-ordinates as a list.

Butterfly Curve
The butterfly curve.

Scattering of colored flower petals.

Rose Curves
Various rose curves.

Archimedies, Fermat and logarithmic spirals.

Entwined logarithmic spirals of a sunflower head.

Twisted Rose Curve
Various twisted rose curves.

Twisted R C Anim
A series of 20 twisted curves.