# Thread: Interior points of a cardioid in complex analysis

1. ## Interior points of a cardioid in complex analysis

Is there a formula for the points that are contained in the main cardioid of the Mandelbrot set?

The boundary of the cardioid is given by,

$c = \frac{1 - (e^{it} - 1)^2}{4}$ which I have seen many times although I have never seen what the 't' stands for...

However this just plots the perimeter.

How could I change this to find a formula for every point contained in the cardioid? Would it just be something simple like putting absolute value signs on both sides and changing the = to a $\leq$?

Haven't though that through but was the first thought that came to my head however I'm pretty sure it's wrong...

Is there a formula for the points that are contained in the main cardioid of the Mandelbrot set?

The boundary of the cardioid is given by,

$c = \frac{1 - (e^{it} - 1)^2}{4}$ which I have seen many times although I have never seen what the 't' stands for...

However this just plots the perimeter.

How could I change this to find a formula for every point contained in the cardioid? Would it just be something simple like putting absolute value signs on both sides and changing the = to a $\leq$?

Haven't though that through but was the first thought that came to my head however I'm pretty sure it's wrong...
EDIT: I completely misread this, I will come back if I remember and try to answer it.

3. I'm gonna bump this to the top seeing as the above answer has taken away my 'unanswered thread' status!