Here's a program that takes complex values with modulus
1 (from the complex unit circle)
and plugs them into EQ (a polynomial in X)
and plots the result.  You can get some neat spirographic results
with the right polynomial.  '1.5*INV(X)+4.5*x' draws an ellipse for instance.
The program doesn't erase the plot screen, so that you can overlap plots
of different functions.  A simple erasing program can be created to erase the
screen separately: ERS: \<< ERASE \>>

A neat exercise for students would be to find what coefficients are needed
on the terms of '1/X + X' to get an ellipse with major and minor axes a,b.

A 4-leaf rose is produced by '(0,-1.5)*(x^3-INV(X))'

Simple polynomials such as 'X+.2*X^4' act like a point on a spining circle
that is attached to another spining circle.  Kind of like the models that were
tried for planetary motion.

Some technical notes:  Instead of looping on theta, I used multiplication by
a complex number that represents a small angle to bump the sampling point
around the circle.

Also used leftarrow in the local variable that serves as the independent var
so that I didn't have to use a global variable.  In a programming sense,
a local variable with a \<- at the beginning of its name, acts as a global
variable.  So I just use the (up arrow)MATCH command to replace X with \<-x
in the EQ, stored as eq locally.

Use left-shift alpha to get lower case letters.
--------

Notation:

\<< means left double angle bracket
\-> means right arrow
\<- means left arros
\>> means right double angle bracket
\|^ means up arrow

Program:
 
\<< '(COS(.05),SIN(.05))'
\->NUM (1,0) 0 \-> inc
\<-x eq
  \<< EQ { X \<-x }
\|^MATCH DROP 'eq'
STO { # 0d # 0d }
PVIEW eq EVAL 0 126
    START eq EVAL
DUP 3 ROLLD LINE \<-x
inc * '\<-x' STO
    NEXT DROP
  \>> 7 FREEZE
\>>