A long time ago I discovered the 4-pointed astroid.
I was able to make it sharp by changing the exponent to any odd number greater than 3. It gets sharper and sharper with 5, 7, 9, etc., but I find 5 to be the most aesthetically pleasing. It looks like a nice 4-pointed star.
Now what I want to do is make it a 5-pointed astroid. I found a formula at wikipedia and entered it:
However, it's not sharp. I want to give it the same sharpness as I did when improving the plain 4-pointed astroid. I played around with the formula for a long time, but could not get what I want. I tried adding exponents to the s, to each cos/sin, to the whole formula, but never figured it out.
I'm afraid I don't know much about graph transformations in the parametric system. Does anyone know how to do it?