Using Parametrics to Draw a Picture Advice

[Skyler0114]

Disclaimer: Even though this problem originates from a project I was given in a math class, it doesn't really follow the format of any homework assignment and is really much more about general math question.
In my math class I was given a project to draw an image with parametric equations.
I want to have a bit of fun with this. I was looking into doing a simplified version of starry night based off this picture:

I have to represent my drawing with a single equation, but I can define different equations on different intervals of t, so that's not a real problem.
I wanted to ask several general questions to get this project underway.
1. are there any programs you guys can point me to in order to graph a lot of parametrics each on different intervals of t.
2. are there any functions you guys can think of that approach 1 for a very small interval of t and is almost 0 for all other intervals of t.
3. same as second except approaches t and is 1 at all other values.
4. same as second except approaches t and is 0 at all other values.
5. Any ideas for a good set of general parametric functions to represent each petal in the tower. A function that I can then modify the intervals/equations to make most of the rest.

 

[fresh_42]

A graphic program to draw functions and relations such as graph.exe should do, but to insert all those tiny fractions is cruel. And don't you need two parameters instead of just one? You can code the entire picture by polygons, spiral or circle fragments etc., but that seems not really manageable.

Maybe it's faster to generate a binary scan and encode the result.