Background
I’m doing exercise 4.9 of Think Julia, which asks for a function for a polar rose using Luxor’s turtle graphics.
Difficulties
 Work out the geometric structure of the family of polar roses. The key is
to construct some auxiliary isoceles triangles and work out the angles between
them. One sees that they are parametrized by two varaibles
n
andk
.n
: number of petalsk
: petal increment constraint:
k ≠ n ÷ 2
 Handle the case when
gcd(n, k) > 1
, i.e. more than one closed loop.  The positive
x
direction goes to the right; the positivey
direction goes down.
Attempt
 Use
ThinkJulia.Reposition(t::Turtle, x, y)
to reposition the turtle.  Use
turn(t::Turtle, θ)
to turnt
 Use
ThinkJulia.Orientation(t::Turtle, θ)
to restore the turtle’s orientation after the move.
Code
I spend three days writing and testing this function.


To test this function, one can issue a few lines.
include("polar_rose.jl"); 🐢 = Turtle();
@svg begin
polar_rose(🐢, 8, 3, 100)
end
Solution
The book’s solution is much simpler than mine. I’ve overthought this problem by
thinking about the “petal increment”, concentric petal curves and closed loops.
The author simply draws one single petal with an auxiliary function
petal (t::Turtle, r, angle)
, which is a simple for
loop.
function petal(t, r, angle)
for i in 1:2
arc(t, r, angle)
turn(t, angle180)
end
end
The logic behind this loop is that arc(t::Turtle, r, angle)
turns t
’s
orientation by angle
degrees due to the line turn(t, angle)
in the
function polyline(t::Turtle, n, len, angle)
called by arc(t, r, angle)
.
function polyline(t, n, len, angle)
for i in 1:n
forward(t, len)
turn(t, angle)
end
end
N.B.: Since the y
axis is inverted in Luxor, so as the sign of an angle.