Animation Generated Using the XY Function

z = k (x2 + k2xy + y2)

k is implemented as z_factor, k2 as xy_factor.

This was generated by varying xy_factor (k2) from -1 to 4.8 in steps of 0.2 with z_factor (k) set to 0.01. The colour map is orange and black.

pat.createColourMap(ColourMap.orange,ColourMap.black,2)
pat.setSize (400,300)
pat.z_factor=0.01
pat.filename='circle'
pat.fun=pat.xyfun
pat.drawXYSequence(-1, 0.2, 1, 30)

Here's another animation from the same sequence, but concentrating on the region close to k2 = 2, where the pattern switches from elliptical to hyperbolic.

The next pattern was generated using 16 colours from orange to black, k = 0.0251 and k2 = 3.