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 thats 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.