I'm learning L-systems and have been reading the book Algorithmic Beauty of Plants by Aristid Lindenmayer.

In the book they discuss the use of rotation matrices for the turtle geometry used to traverse and draw the L-systems in 3-dimensions.

Their definition of rotation matrices:

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The wikipedia page for Rotation matrix defines it as:

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Notice on the x,h matrices they are identical, but for u,z and y,l there are sin(a) that have negatives swapped.

Is this an intentional alteration for the purposes of turtle geometry or does the negative sign not have a significant alteration to how the rotation is applied?

  • 2
    $\begingroup$ Representation of a rotation by a matrix is not unique. $\endgroup$
    – Randall
    Nov 26, 2022 at 21:20
  • 1
    $\begingroup$ The swapped negative sign just means a rotation in the opposite direction, on that plane. $\endgroup$ Nov 26, 2022 at 21:21

1 Answer 1


Remember that $$\sin(-\alpha)=-\sin\alpha.$$


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