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NCB Deposit  # 139


Dr. Cye Waldman

cye@att.net


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Voderberg Deconstructed and Triangle Substitution . . . .

A Family of Tilings
Voderberg

Click here to see a full "pdf" file with Matlab code for Voderberg and Triangle Substitution Tilings.





Voderberg animation


Voderberg4



Voderberg3



Vodeberg5


Bent Wedge


We apply the equations for a generalized Voderberg tile that is parameterized in terms of a single angle;  all segment lengths and internal angles can be expressed in terms of it.  We then demonstrate how to turn those lengths and angles into a tile in the complex plane.  Finally, we apply a method of triangle substitution to create original radial and spiral tilings.  For more information be sure to read the attached "pdf" file.
Dr. Cye Waldman


Copyright Notice:  This animation and all images within are under copyright by Cye Waldman and may not be copied, electronically or otherwise, without his espress permission.
Dr. Cye Waldman
cye@att.net

Voderberg
References
Other Waldman contributions to the NCB:
Sinusoidal Spirals:  < http://curvebank.calstatela.edu/waldman/waldman.htm >
Bessel Functions    < http://curvebank.calstatela.edu/waldman2/waldman2.htm >
Gamma Funcions   < http://curvebank.calstatela.edu/waldman3/waldman3.htm >
Polynomial Spirals and Beyond   < http://curvebank.calstatela.edu/waldman4/waldman4.htm >
Fibonacci and Binet Spirals with a touch of Mondrian  < http://curvebank.calstatela.edu/waldman6/waldman6.htm >
"Other" Fibonacci Spirals and Binet Spirals  < http://curvebank.calstatela.edu/waldman7/waldman7.htm >
A Mathematician's Valentine < http://curvebank.calstatela.edu/waldman8/waldman8.htm >
The NCB thanks Dr. Waldman for his strong contibutions.

Other spiral Deposits in the NCB:
< http://curvebank.calstatela.edu/spiral/spiral.htm >
< http://curvebank.calstatela.edu/log/log.htm >

Other Cardioid - Valentines -  in the NCB:
< http://curvebank.calstatela.edu/index/cardioid.gif

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