In the text $($on pp$.158159),$ we developed this function to draw fractal trees $($note that some printings of the text contain a typo on p$.159$the function name $$drawTree$$ on the second and fourth lines from the top of the page should read $$fractalTree$$ as shown in the corrected code below$)$:

def fractalTree$($trunkLength$)$:

$$ if trunkLength $<10$:

$$ return

$$ else:

$$ turtle.forward$($trunkLength$)$

$$ turtle.left$(45)$

$$ fractalTree$($trunkLength$/2\mathrm{.}0)$

$$ turtle.right$(90)$

$$ fractalTree$($trunkLength$/2\mathrm{.}0)$

$$ turtle.left$(45)$

$$ turtle.backward$($trunkLength$)$

This function draws trees with a fixed angle $(45$ degrees$),$ always decreases their trunk length by a factor of $2,$ and stops when trunkLength becomes less than $10.$

Your task is to write a more flexible function fractalTree$2($angle$,$ scale, trunkLength, levels$).$ fractalTree$2$ takes the angle as an argument. It also takes scale, which specifies an amount by which we multiply trunk length as we go from one level to the next $($i$.$e$.,$ if we set the scale to $0\mathrm{.}5,$ it will cut trunkLength in half at each level$).$ It also uses the variable levels to determine how many levels to go before stopping.

$$

Here's an example:

$>>>$ fractalTree$2(45,0\mathrm{.}75,100,4)$

If you would like to$,$ you can customize your recursive drawings with other features $($colors$,$ etc.$).$