What is a Basic Ferguson Function? Surely z2+c the Mandelbrot Set is a basic function.
Ferguson Novas are a special kind of function, where the Ferguson Nova is attached to a bigger manikin having spirals outside.
The basic Ferguson Nova Function is: \(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^3 - 1}{z} }\)
The general basic Ferguson Nova Function is: \(\mathbf{\bf\:z - \mit{factor*}\bf\:\cfrac{z^{n+2} - 1}{z^n} }\)
In the table first the standard Tierazon2 rendering is shown, then a rendering to enhance the look of the spirals.
In the table scaled 1.0 is the scale value of the function: scale*f(z,c): 1.0*f(z,c).
In the table s=0.25 is the start value 0.25 of the iteration. Please see math basics.
Clicking on the thumbnail image, a large version is shown.

basicFerguson01

scaled 1.0
s=0.22617924
basicFerguson01

scaled 1.0
s=0.22617924
basicFerguson02

scaled 1.0
s=0.471695
basicFerguson02

scaled 1.0
s=0.471695
basicFerguson03

scaled 1.0
s=0.6325834
basicFerguson03

scaled 1.0
s=0.6325834
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^3 - 1}{z} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^3 - 1}{z} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^4 - 1}{z^2} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^4 - 1}{z^2} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^5 - 1}{z^3} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^5 - 1}{z^3} }\)
basicFerguson04

scaled 1.0
s=0.7359461
basicFerguson04

scaled 1.0
s=0.7359461
basicFerguson05

scaled 1.0
s=0.8048797
basicFerguson05

scaled 1.0
s=0.8048797
basicFerguson06

scaled 1.0
s=2.46264186
basicFerguson06

scaled 1.0
s=1.889881575
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^6 - 1}{z^4} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^6 - 1}{z^4} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^7 - 1}{z^5} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^7 - 1}{z^5} }\)
\(\mathbf{\bf\:z - \mit{0.01*}\bf\:\cfrac{z^8 - 1}{z^6} }\)
\(\mathbf{\bf\:z - \mit{0.01*}\bf\:\cfrac{z^8 - 1}{z^6} }\)
basicFerguson06

scaled 1.0
s=0.67032833
basicFerguson06

scaled 1.0
s=0.67032833
basicFerguson10

scaled 1.0
s=0.947466
basicFerguson10

scaled 1.0
s=0.947466
basicFerguson10

scaled 1.0
s=0.947466
basicFerguson06

scaled 1.0
s=0.67032833
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^8 - 1}{z^6} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^8 - 1}{z^6} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^{12} - 1}{z^{10}} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^{12} - 1}{z^{10}} }\)
\(\mathbf{\bf\:z - \mit{0.05*}\bf\:\cfrac{z^{12} - 1}{z^{10}} }\)
\(\mathbf{\bf\:z - \mit{0.01*}\bf\:\cfrac{z^8 - 1}{z^6} }\)