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Fujimoto approximator

The Fujimoto approximation technique can be used to fold a piece of paper into any odd number of units. It was developed independently by Fujimoto and Brunton, and the mathematics has been explored by Robert J. Lang and Tom Hull.

This utility shows how you can use this technique in your own practical origami projects. You can also use it to experiment with the Fujimoto approximation technique to gain an insight of how it works.

Choose the number of units and enter the initial guess as a fraction of the width of the paper, starting from the left. The default is 0.5. but the closer you get to the true fraction, the faster the sequence will converge. The minimum accuracy percentage is used to determine the precision of the binary number, and the best possible accuracy of the result. The smaller the percentage, the more steps will be used to generate the sequence.Values can be less than 1 e.g (0.5 or 0.01).

Depending on the number of units, not all the divisions will be creased.

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1/    Initial guess: Minimum accuracy % (lower is best):

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Binary fraction = 0.001001

7 steps required

Step 1:

Fold your initial guess at approximately 0.5 of the width of paper starting from the left-hand edge.

Step: 2 - Digit: 0

Fold from the right of the page to the previous crease.

Crease position from left-hand edge = 0.75 - Crease is at 5/7 within 4.762%

Step: 3 - Digit: 0

Fold from the right of the page to the previous crease.

Crease position from left-hand edge = 0.875 - Crease is at 6/7 within 2.041%

Step: 4 - Digit: 1

Fold from the left of the page to the previous crease.

Crease position from left-hand edge = 0.4375 - Crease is at 3/7 within 2.041%

Step: 5 - Digit: 0

Fold from the right of the page to the previous crease.

Crease position from left-hand edge = 0.71875 - Crease is at 5/7 within 0.621%

Step: 6 - Digit: 0

Fold from the right of the page to the previous crease.

Crease position from left-hand edge = 0.859375 - Crease is at 6/7 within 0.260%

Step: 7 - Digit: 1

Fold from the left of the page to the previous crease.

Crease position from left-hand edge = 0.4296875 - Crease is at 3/7 within 0.260%