Once you fit two or more together, you can copy and paste this cluster to start filling the page with a tessellating pattern. 1987), to create a tessellations dual, draw a dot in the center of each shape, connect. If you like, make a third or fourth copy of the shape and fill each copy with another color or design. Monohedral tessellations are made of one shape that is rotated or flipped to form different patterns. Each geometric shape that is tessellated will be written in its own function. Fill it with another color (or change the colors or patterns in the design). In this project, you will make a program that draws some tessellations. Fill the trimmed shape with color (or with a design).Ĩ. We recommend starting with half of a regular 8.5' x 11' white sheet of paper. Select and drag the second wiggly line so that it touches the bottom ends of the two straight lines (or so that it fits inside the two straight lines). Start with a piece of paper and a pencil. Your sketchbook should be set up like the following: Note: If you decide to draw an. Now use the selection tool to drag each straight line so that it touches an end of the wiggly line.Ħ. You will be creating a tessellation based on an original motif drawn by you. Use the selection tool and make a copy of this line, too.ĥ. Copy and paste it nearby so that you have two wiggly lines that are exactly the same.Ĥ. Now, use your selection tool (the "running ants") and click and drag around your wiggly line.ģ. Mark out a LIGHT grid on your paper with the use of the 3 X 3 (7.5 x 7.5 cm) index card you received and a pencil. (Don't put any loops in it!) If you measure straight across from the starting point to the ending point, that should be the widest part of the wiggly line.Ģ. Turtle.Here is one way to make a wavy-line tessellation in any computer drawing program.ġ. Turtle.goto(OUTER_RADIUS / 4, -3 * INNER_RADIUS / 2) Turtle.goto(-OUTER_RADIUS / 2, -2 * INNER_RADIUS / 2) It could be a wiggly line, or zigzags, but dont make the design too complicated to cut out. Turtle.goto(OUTER_RADIUS / 4, -1 * INNER_RADIUS / 2) Begin by drawing a line from the top your card to the bottom. Keeping our initial code the same: screen = Screen() (Increase the depth argument to fill the window.) The tessellation you really want is four (not thirds) of these patterns overlaid atop each other. Turtle.goto(-OUTER_RADIUS / 2, -INNER_RADIUS) Rt_row_2(x-size/2,y+size*math.sqrt(3)/2,size,800//(size*3))įirst, let's simplify your three turtle, three function hexagonal tessellation to a single turtle, single recursive function solution: from turtle import Screen, Turtle Here is code: def draw_rhombus(x,y,degree,size,tilt,color):įor i in range(800//int(round(size*math.sqrt(3)))): After that it is repetition of the first and second row. Then, all output triangles are oriented counterclockwise. Before tessellation, all input data is projected into a plane perpendicular to the normal. The winding number of each resulting region is the number of original polygons that cover it. The figure contains three different rhombus shapes (they are the same rhombus in different orientation). UNION - To calculate the union of several contours, draw all input contours as a single polygon. To be able to fill each rhombus, it needs to be drawn individually. I would draw based the rhombus shape because it will allow you to fill them with different colors. Translate all the points previously constructed on line AB by this vector and then translate the image and the image of the image to get a finite piece of the lattice defined by ABC. However, when I loop the program, the turtles trace back the same path as before and it takes a while for it to draw the others. So far, I created 3 hexagons in the center with 3 turtles and used for loops to draw the hexagons around the 3 hexagons. So far, I'm only alternating the angles of the turtles as I run the program and I don't have a definite strategy. I'm not sure how I can create the hexagon pattern recursively. I thought about creating a hexagon pattern first and then dividing the hexagons into thirds. I'm trying to create a rhombus tessellation pattern with the turtle graphics on python that looks like this image:
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