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Python Turtle drawing circle with squares

Trying to draw this picture using turtle, just stuck on the last bit of drawing square into a circle. squares to make circle
so far I've tried just drawing out the points of each individual line but takes way to long with some inconsistencies. What I have so far is
def square(side_length):
for i in range(4):
turtle.fd(side_length)
turtle.lt(90)
square (150)
turtle.penup()
####New Square###
turtle.left(90)
turtle.forward(75)
turtle.left(90)
turtle.forward(30)
turtle.right(180)
turtle.right(45)
turtle.pendown()
def square(side_length):
for i in range(4):
turtle.fd(side_length)
turtle.lt(90)
square (150)
This draws two squares. Now I just need to figure out a way to rotate the two squares by, say, 30 degrees clockwise 4 times. Is there a function I can use to do this, or do I just need to do a lot of math and calculate to draw each individual line?

Despite its name, turtle.circle can be used to draw other regular polygons. It also can be used to draw only part of the polygon. Combined with picking the pen up and down, you can easily draw a series of rotated shapes sharing the same center.
For example,
for i in range(19):
turtle.circle(100, 360, 4) # draw a square
turtle.penup()
# "draw" 10 degrees of the same circle, with the pen up, just to move the pen
turtle.circle(100, 10, 4)
turtle.pendown()
(The circle is just a polygon with enough sides to approximate a circle. If you don't specify the third argument explicitly, turtle picks a sufficiently large value based on the radius.)

It's a combination of the two. You need to do a little math to find the starting point for each square. However, once you move the turtle to that point and turn it to the correct heading, your block of statements to draw the four sides will work just fine.
After you draw the last side of a square, the turtle is sitting on the outer circle, facing 45 degrees off a radius to that point.
Turn the turtle 60 degrees to face across a shallow chord of the circle.
Move it the appropriate distance to traverse that chord (this is where your math comes in).
Turn the turtle another 60 degrees. You are now ready to draw the next square.
Repeat those steps for each added square.

How to put the figure inside a circle using turtle?

I got a simple figure using turtle. But the problem is I dunno how to put that figure inside circle.
Code:
import turtle
painter = turtle.Turtle()
painter.pencolor("blue")
for i in range(50):
painter.forward(100)
painter.left(123*2)
painter.circle(70)
turtle.done()

A bit of trigonometry in my head and I figured the angle. Not sure if I got the radius correct though. Ideally figure out the coordinates of the center instead, but a quick and dirty solution is:
import turtle
painter = turtle.Turtle()
painter.pencolor("blue")
for i in range(50):
painter.forward(100)
painter.left(123*2)
painter.right(123)
painter.right(90)
painter.penup()
painter.forward(10)
painter.left(90)
painter.pendown()
painter.circle(70)
turtle.done()

You will need to move the turtle to the correct starting position. NOTE that's not the circle's center! It starts drawing the circle from its rightmost position - i.e., if you want a circle with radius 70 around (0,0), then move to (70,0), e.g.:
painter.penup()
painter.goto(70,0)
painter.pendown()
painter.circle(70)
FYI: I can't immediately figure out where the center of your drawing is, but I suspect it is NOT at (0,0). In all cases, you should place the turtle to the right of your shape's center, offset by the circle's radius, to make the circle go around it.

Another approach would be to average the positions of your arbitrary image and then use that average as the center of the surrounding circle:
from turtle import Screen, Turtle, Vec2D
CIRCLE_RADIUS = 70
POLYGON_LENGTH = 100
POINTS = 50
screen = Screen()
painter = Turtle()
painter.speed('fastest')
painter.pencolor("blue")
total = Vec2D(0, 0)
for _ in range(POINTS):
painter.forward(POLYGON_LENGTH)
total += painter.position()
painter.left(246)
x, y = total * (1.0 / POINTS) # Vec2D can multiply by scalar but not divide
painter.penup()
painter.goto(x, y - CIRCLE_RADIUS)
painter.setheading(0)
painter.pendown()
painter.circle(CIRCLE_RADIUS)
screen.exitonclick()

Python Turtle: Draw concentric circles using circle() method

I was showing a grandson patterns drawn with Python's Turtle module,
and he asked to see concentric circles.
I thought it would be faster to use the turtle's circle() to draw them
than to write my own code for generating a circle. Ha! I am stuck.
I see that the circle produced begins its circumference at the turtle's
current location and its direction of drawing depends on turtle's current
direction of motion, but I can't figure out what I need to do to get
concentric circles.
I am not at this point interested in an efficient way of producing
concentric circles: I want to see what I have to do to get
this way to work:
def turtle_pos(art,posxy,lift):
if lift:
art.penup()
art.setposition(posxy)
art.pendown()
def drawit(tshape,tcolor,pen_color,pen_thick,scolor,radius,mv):
window=turtle.Screen() #Request a screen
window.bgcolor(scolor) #Set its color
#...code that defines the turtle trl
for j in range(1,11):
turtle_pos(trl,[trl.xcor()+mv,trl.ycor()-mv],1)
trl.circle(j*radius)
drawit("turtle","purple","green",4,"black",20,30)

You can do it like this:
import turtle
turtle.penup()
for i in range(1, 500, 50):
turtle.right(90) # Face South
turtle.forward(i) # Move one radius
turtle.right(270) # Back to start heading
turtle.pendown() # Put the pen back down
turtle.circle(i) # Draw a circle
turtle.penup() # Pen up while we go home
turtle.home() # Head back to the start pos
Which creates the picture below:
Basically it moves the turtle down one radius lenght to keep the center point for all the circles in the same spot.

From the documentation:
The center is radius units left of the turtle.
So wherever the turtle is when you start to draw a circle, the center of that circle is some distance to the right. After each circle, just move left or right some number of pixels and draw another circle whose radius is adjusted for the distance the turtle moved. For example, if you draw a circle with a radius of 50 pixels, then move right 10 pixels, you would draw another circle with a radius of 40, and the two circles should be concentric.

I am not at this point interested in an efficient way of producing
concentric circles: I want to see what I have to do to get this way to
work
To address the OP's question, the change to their original code to make it work is trivial:
turtle_pos(trl, [trl.xcor() + mv, trl.ycor() - mv], 1)
trl.circle(j * radius)
becomes:
turtle_pos(trl, [trl.xcor(), trl.ycor() - mv], 1)
trl.circle(j * mv + radius)
The complete code with the above fix and some style changes:
import turtle
def turtle_pos(art, posxy, lift):
if lift:
art.penup()
art.setposition(posxy)
art.pendown()
def drawit(tshape, tcolor, pen_color, pen_thick, scolor, radius, mv):
window = turtle.Screen() # Request a screen
window.bgcolor(scolor) # Set its color
#...code that defines the turtle trl
trl = turtle.Turtle(tshape)
trl.pencolor(pen_color)
trl.fillcolor(tcolor) # not filling but makes body of turtle this color
trl.width(pen_thick)
for j in range(10):
turtle_pos(trl, (trl.xcor(), trl.ycor() - mv), True)
trl.circle(j * mv + radius)
window.mainloop()
drawit("turtle", "purple", "green", 4, "black", 20, 30)

So now i am giving you the exact code that can draw concentric circles.
import turtle
t=turtle.Turtle()
for i in range(5):
t.circle(i*10)
t.penup()
t.setposition(0,-(i*10))
t.pendown()
turtle.done()

How to create a color wheel using turtle graphics?

I am trying to create somewhat of a color wheel using the turtle module in Python. Let's say I have a list of colors:
colors = ["#880000","#884400","#888800","#008800","#008888","#000088",
"#440088","#880088"]
I am aiming to go around a circle with a radius of 250px plotting in the colors:
def drawColors():
for color in colors:
turtle.color(dark)
for i in range(len(colors)):
turtle.begin_fill
turtle.circle(150)
turtle.end_fill()
turtle.done()

You can do it by dividing the circle up into multiple circular sectors (aka pie slices) and drawing each one in a different color. The tricky part doing it with turtle graphics is setting the initial position and heading (or direction) of the turtle to be at the start of the arc of each one. Also, unlike with the case with a full circle, you need to manually close the figure before filling it by drawing the final line segment from the end of the arc back to the center of the circle.
While this could be calculated mathematically, doing that is avoided in the following code by remembering, for all but the first sector, where the previous one left off and using that as the starting position and heading for the next. Fortunately for the initial one, these values are relatively simple to compute: the position is set to the (circle_center x value + radius, circle_center y value) with a due North heading of 90°.
import turtle
colors = ['#880000','#884400','#888800','#008800',
'#008888','#000088','#440088','#880088']
def draw_color_wheel(colors, radius, center=(0, 0)):
slice_angle = 360 / len(colors)
heading, position = 90, (center[0] + radius, center[1])
for color in colors:
turtle.color(color, color)
turtle.penup()
turtle.goto(position)
turtle.setheading(heading)
turtle.pendown()
turtle.begin_fill()
turtle.circle(radius, extent=slice_angle)
heading, position = turtle.heading(), turtle.position()
turtle.penup()
turtle.goto(center)
turtle.end_fill()
draw_color_wheel(colors, 150, center=(25, 50))
turtle.hideturtle()
print('done - press any key to exit')
turtle.onkeypress(exit)
turtle.listen()
turtle.done()
Result

Since this question has become active again, let's solve it using stamping rather than drawing:
from turtle import Turtle, Screen
colors = ['#880000', '#884400', '#888800', '#008800',
'#008888', '#000088', '#440088', '#880088']
def draw_color_wheel(colors, radius, center=(0, 0)):
slice_angle = 360 / len(colors)
yertle = Turtle(visible=False)
yertle.penup()
yertle.begin_poly()
yertle.sety(radius)
yertle.circle(-radius, extent=slice_angle)
yertle.home()
yertle.end_poly()
screen.register_shape('slice', yertle.get_poly())
yertle.shape('slice')
yertle.setposition(center)
for color in colors:
yertle.color(color)
yertle.stamp()
yertle.left(slice_angle)
screen = Screen()
draw_color_wheel(colors, 250, center=(25, 50))
screen.exitonclick()
OUTPUT
This approach takes slightly less code and produces noticeably faster output.

Python - Make One Turtle Object Always Above Another

I would like to create a program where one Turtle object always stays above all of the other Turtle objects. I don't know if this is possible, but any help would be apprecated.
This is my code:
from turtle import *
while True:
tri = Turtle()
turtle = Turtle()
tri.pu()
tri.pencolor("white")
tri.color("black")
tri.shape("turtle")
tri.bk(400)
turtle = Turtle()
turtle.pu()
turtle.pencolor("white")
turtle.shape("square")
turtle.color("white")
turtle.pu()
turtle.speed(0)
tri.speed(0)
turtle.shapesize(100,100,00)
setheading(towards(turtle))
while tri.distance(turtle) > 10:
turtle.ondrag(turtle.goto)
tri.setheading(tri.towards(turtle))
tri.fd(5)
clearscreen()

Why not just do all the drawing for the "bottom" turtle first? Then do the drawing for the "top" turtle? This should make the top turtle always visible.

My Observed Rules of Turtle Layering:
Multiple Turtles moving to same location: last to arrive is on top.
Same thing drawn by multiple turtles: there are no rules!
To illustrate my second point, consider this code:
from turtle import Turtle, Screen
a = Turtle(shape="square")
a.color("red")
a.width(6)
b = Turtle(shape="circle")
b.color("green")
b.width(3)
b.goto(-300, 0)
b.dot()
a.goto(-300, 0)
a.dot()
a.goto(300, 0)
b.goto(300, 0)
screen = Screen()
screen.exitonclick()
Run it and observe the result. On my system, the final goto() draws a long green line over the red one but the green line disappears as soon as it has finished drawing. Comment out the two calls to dot() and observe again. Now the green line remains over the red one. Now change the calls from dot() to stamp() or circle(5) instead. Observe and formulate your own rule...
Now back to your example, which is badly flawed (you're actually manipulating three turtles, not two!) Here's my simplification:
from turtle import Turtle, Screen
tri = Turtle(shape="turtle")
tri.color("black")
tri.pu()
turtle = Turtle(shape="square")
turtle.shapesize(4)
turtle.color("pink")
turtle.pu()
def drag_handler(x, y):
turtle.ondrag(None)
turtle.goto(x, y)
turtle.ondrag(drag_handler)
turtle.ondrag(drag_handler)
tri.bk(400)
while tri.distance(turtle) > 10:
tri.setheading(tri.towards(turtle))
tri.fd(5)
screen = Screen()
screen.mainloop()
You can tease tri by dragging the pink square until tri catches up with it. Ultimately, tri will land on top as long as the square isn't moving when tri catches it. If you drag the square over tri, then it will temporarily cover him as it is the "last to arrive".