How to Draw a Hilbert Curve

Step-by-Step Guide

1. 1

   Step 1: Gather your materials.

   Refer to the list of Things You'll Need below.
   
   Note that graph paper isn't necessary, but it is very hard to draw a neat fractal without at least lined paper. , It is best to start in the upper-left corner, as it is easier to expand the pattern down and to the right.
   
   Note how you have four figures: two standing upright, next to each other, and two laying on their side, with the upside facing inwards. , You should now have a continuous line from the bottom left, going up and then down, to end in the lower right corner. , This means you draw the same pattern next to it (red), rotate the paper 90° counterclockwise, draw the same pattern again (green), rotate the paper 180° degrees, and draw the pattern again (brown). , Look at how you connect the two upper curves in the middle, at their bottoms, the lower-right curve with the upper-right in the middle on the right side, and the lower-left curve with the upper-left in the middle, on the left side.
   
   This is always the same. , The one show in the picture is a 4th order Hilbert curve.
   
   You can fit a 5th order Hilbert curve on a regular sheet of A4 graph paper. , You could draw each next order in a different colour, as in the picture, or just make up your own way of colouring this beautiful fractal.
2. 2

   Step 2: Copy the pattern seen in the picture.

3. 3

   Step 3: Connect the 'legs' of the figures.

4. 4

   Step 4: Copy the resulting pattern as if it were the first one.

5. 5

   Step 5: Connect the loose ends again.

6. 6

   Step 6: Repeat the pattern over and over again

7. 7

   Step 7: as much as you want to.

8. 8

   Step 8: Colour your fractal to your liking.

Detailed Guide

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