| How to Draw the Golden Spiral Dec 26th 2012, 16:00 The golden spiral is a well known shape. Commonly found in nature, the golden spiral is unique in that it's made using the elements of the Fibonacci sequence. It is fairly simple to draw one, and can be quite beautiful when done correctly.
- Visualize a system of squares that will end up "inscribing" the spiral. Gather your materials, making sure that you have everything––the list of what is needed is found below. Read all of the steps before attempting to begin the drawing process.
- Locate your first squares: 1X1, 1X1 and 2X2. Draw them by drawing a sort of a whirlpool of squares. You can express this process as: "squares of the numbers of the Fibonacci sequence 'describe' the Golden Spiral mathematically".
- Experiment using a regular sheet of graph paper turned sideways (landscape), following the steps. If the graph paper has 1/4 inch squares, then the 1 by 1 square at (30, 12), 30 across and 12 up from the bottom left will probably center the spiral.
- Mark each square by drawing a box around it. Start with the second square to the left, then down, then right, and up, on around counterclockwise, step by step on the graph paper.
- Use the Fibonacci sequence. This works by adding the two previous numbers: You get the next one starting from 0 and 1; so, it goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
- The length of one side of each square should equal a number in the sequence (the 0 is not needed for drawing any of the square), but the beginning point can be called (0,0), if we set it up that way. You will have a 1X1 square with a second 1X1 drawn next to it on the left side of the first, then down to put 2X2, and right for 3X3, then up for 5X5, and then left to fit 8X8. Below all that, put 13X13 and so on, to as large a square as your paper can fit.
- Draw each of these squares in a counter-clockwise pattern. It will finally form a spiral as you draw a curve through the squares (as instructed later).
- Draw squares with side lengths of 21, 34, 55. Here 55 is the largest one shown. 21X21 may reach the maximum size on the sheet of the graph paper suggested.
Draw the spiral - Take your compass and put it as shown in the picture, with its length set at one unit (side of the first square) long. Turn it 90 degrees counter-clockwise.
- Adjust the compass so it is now two units long. Again, turn it 90 degrees counter-clockwise. Then 3, then 5, next 8 and continue this process until the squares each have the curving spiral through them.
- Take your pen and carefully trace along the curve. If you're shooting for exceptional accuracy, you can use a French curve to help you.
- With the spiral traced in pen, use your eraser to rub out the squares made in pencil.
- Congratulations, you've just made the golden spiral!
- Using a French curve can greatly help your accuracy, but it takes some practice to find the right curves and make it flow.
- Use a thick pen. It gives you a bit more "wiggle room" with the pencil curve, so if you start to stray a little you can catch it and correct it without it being too obvious.
Edit Warnings - Be careful with compasses. They can rip your paper, and the base is quite sharp.
Edit Things You'll Need - Graph paper
- Compass
- Pencil
- Eraser
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