| K (scheme #) | M > 1 (repelling pt) |
0 < M < 1 (attracting pt) |
-1 < M < 0 (attracting pt) |
M < -1 (repelling pt) |
| 1 | red dot | yellow dot | pink dot | purple dot |
| 4 | red plus sign | yellow little square | pink bigger square | purple minus sign |
| 5 | fat red dot | fat yellow dot | fat pink dot | fat purple dot |
| 7 | dark red dot | brite white dot | brite white dot | dark red dot |
| 0 | red dot | purple dot | purple dot | red dot |
Other color schemes are as follows:
K=2: The slope M is used, but now steep positive slopes get dark reds; as the slopes level off, the colors progress towards yellow and then white. As the slopes become negative, the colors darken again, through blues and purples.
K=3: Here the prime period of the point defines the color; when pALL is used, this makes it easy to identify which curves identify points of which prime periods. K=8 does the same thing, using thicker dots.
K=6: Points of prime period N alone are shown brightly; points of lesser periods appear dark (using pALL or pDIV)
Now, for pORG, there are a few differences.
First is, that all slopes are computed using f ^N (where N
is the value of "iterate" set by the user) instead of
f ^k, where k is the prime period of the point.
That said, K=0,1,4,5 and 7 work as for
pPRM,
pALL, and
pDIV.
K=2 again uses varying colors but chosen slightly differently. K=6 just
plots all points in the same color.
K=3 is the only new one. Here at every point (C,x) on the screen,
the color is chosen based on how far f_C(x) is from the Nth iterate of
f_C(x). An example is shown below, with N=4. The outline of the
"k|4" picture (all period 1,2,4 prime periodic points) is clearly visible.
|
Return to Chip's Home Page
Return to CMJ Article Page Return to "orbits" help file, Page 2 |
© 2001 by Chip Ross Associate Professor of Mathematics Bates College Lewiston, ME 04240 |