8-Bit Software Online Conversion

Mathematician Peter Maurer made public the simple algorithm that is used to produce these pictures. (Ref. The American Mathematical Monthly, Volume 94,pp631-645.) For obvious reasons the algorithm referred to is known as "The Rose". Here, in terms that can easily be transcribed to any standard computer language, is what you have to do to produce such pictures on your own computer. The program uses whole number variables N, D and A, and real number varibles X, R, oldX, oldY, newX, newY. At the start of the program, set the variables N and D equal to two whole numbers between 1 and 359 (inclusive), and set A, oldX, and oldY equal to zero. Now you set up a loop consisting of the following steps. 1. SetA equal to A+D. If A>360 replace A by the remainder obtained when you divide A by 360 (that is compute A mod 360 and set A equal to the result). 2. Calculate N*A, then reduce it mod 360(i.e. take the remainder on dividing N*A by 360), convert the result from degrees to radians, and set X equal to the final result. (To convert from degrees to radians, multiply by 0.01745.) 3. Set R equal to the sine of X. 4. Convert A from degrees to radians, and set T equal to the result. 5. Set newX equal to R*sin(T) and set newY equal to R*cos(T). (This converts the polar coordinates (R,T) to rectangular coordinates (newX,newY).) 6. Draw a line from the point(oldX,oldY) to (newX,newY). 7. If A is equal to zero, then stop, else set oldX equal to newX, oldY equal to newY, and go back to step one. The only input the program requires are values for the two integer variables N and D. Different choices of these two numbers produce often strikingly different patterns. For some choices the pattern turns out to be fairly rudimentary, sometimes just a single dot. For other values you will obtain pictures every bit as attractive as these: Enter N=4, D=43 or N=5, D=97. They may not smell as sweet, but the roses you produce on your computer screen can bring every bit as much pleasure as the real thing. p.s. Keith Devlin is a professor of mathematics. He formerly worked in this country but now lives in the United States. Margaret Wright. K3X