Quite BASICBifurcationsThis short program shows how the logistic map converges to different stable orbits depending on the value of the parameter R. At certain values of R, the number of points in the orbit changes. Those are called bifurcation points. The seemingly simple recursive formula x_n+1 = x_nR(1-x_n) leads to surprisingly rich mathematics. If you want to learm more about bifurcations in the logistic map, you can check out this Wikipedia article.Quite BASIC is a BASIC interpreter written in Javascript and it looks like either your browser doesn't support Javascript or Javascript is disabled. This means that the site will not function properly. We recommend newer versions of IE or Firefox. On Macs, use Safari or Firefox, and on Linux systems we recommend Firefox. Opera should work too.

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Bifurcations

This short program shows how the logistic map converges to different stable orbits depending on the value of the parameter R. At certain values of R, the number of points in the orbit changes. Those are called bifurcation points. The seemingly simple recursive formula x_n+1 = x_nR(1-x_n) leads to surprisingly rich mathematics. If you want to learm more about bifurcations in the logistic map, you can check out this Wikipedia article.

Output

Canvas

BASIC Program

CLS
PRINT "Bifurcations in the Logistic Map"
PRINT "x = r * x * (1 - x)"
LET X = 0.5
FOR R = 2.4 TO 4 STEP 1.4/125
GOSUB 5000
NEXT R
END
REM Iteration subroutine
REM First iterate 50 times to settle into a stable period
FOR I = 1 TO 50
LET X = R * X * (1 - X)
NEXT I
REM Next, iterate 50 more times and plot the points
REM of the stable period
FOR I = 1 TO 50
LET X = R * X * (1 - X)
PLOT (R - 2.4) / 1.6 * 125, X * 125
NEXT I
RETURN
      
  

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