You should complete Exercises $2$ and $3$ from the online spreadsheet tutorial for Module $5($Growth Creates Form$)$ before attempting this question. In fact, if you have completed these exercises, then you should have a solution to this question that requires only very minor modifications prior to submission.

$1$

The bracketed L$-$Grammar used to generate the branching structure shown in $[1,$ Figure $1\mathrm{.}24($e$)]$ is not suitable for use in Excel for the reasons described in the spreadsheet tutorial. We shall use a slightly different version, which is the L$-$Grammar shown over the page: Modified version of L$-$Grammar: $w_0$:$x$

$r_0$:$FFFF{r}_1$:$xF+x--$

$x+$FxUFFU

$($a$)$ Use the method of Exercise $2$ from the spreadsheet tutorial to make a rules table and a rewriting table for the above grammar. Use your rewriting table to find the strings $w_1,w_2,w_3,w_4,w_5$ and $w_6.$ Make sure that the rules are applied in the order $r_0$ followed by $r_1$ at each rewrite. $($So the inner SUBSTITUTE$()$ should apply rule $r_0$ and the outer SUBSTITUTE$()$ should apply rule $r_1.)$

$($b$)$ Use the method of Exercise $3$ from the spreadsheet tutorial to make a turtle settings table and a turtle graphics calculation table for the string $w_5$ you calculated in $($a$).$ As in the tutorial, the starting state of the turtle should be $(0,0,90).$ But for this L$-$system we use a different turn angle $=39\mathrm{.}5.($Make sure that your turtle graphics calculation table is long enough for $w_5.$ You will need to drag down your formulas for over $2500$ rows!$)$

$($c$)$ Plot the $x$ and $y$ columns of your turtle graphics calculation table as an $"x-y$ scatter" chart with lines but no dots. Your picture may be hard to interpret if you use a different format $($and you will lose marks$).$ Make sure the chart is located near the top of your sheet.