Iteration
From Ultrafractal Wiki
Iteration is the repeated application of a function or process in which the output of each step is used as the input for the next iteration.
from: [1]
For an example of use of 'Some Iterations': Selecting a Single Fractal Element for an Image
Hi Everyone,
This isn't an important question except that I'm curious.
I was wondering why, if I set iterations for 2 and start at 15, I get a picture, but, if I set iterations to 1, I don't get a picture starting at either 15 or 16.
(No copyright... I am just fiddling while taking down notes for a sort of standard procedure I could follow.)
Diane Walker
***
One of the upcoming challenges will deal with limited iterations. They can be tricky. Notice that there are a number of settings:
1. Start iteration: this is the first iteration that will be visible
The next two parameters set up the loop characteristics
2. Trap iterations: number of iterations trapped (i.e. visible) in each loop.
3. Skip iterations: after the trapped iterations are executed, this parameter gives the number of iterations that will now be skipped (i.e. not visible) in each loop.
4. Loop count: number of times the trap/skip loop values are repeated (until maxiter or some other terminating value is reached)
When you set trap iterations = 1, given the other parameter settings, you will see iteration 15 only. With trap iterations = 2 you will se iteration 15 and iteration 16 together (and no other iterations). This is because skip iterations = 333, which is larger than maxiter, so only one loop is executed even though loop count = 1e20.
The UPR that I provided the first time used "some iterations" to change the color and that is probably not the best example for it. To really take advantage of "some iterations", change the coloring parameters, like the trap shape. The trick to using Some Iteration is to recognize the pattern. Below, 1 means show the iteration, 0 means skip the iteration. In the UPR below, each layer is set to Trap Iteration = 1, Skip Iteration = 2, but the Start Iteration value is 0 for layer 1, 1 for layer 2, 2 for layer 3, 3 for layer 4. Changing the Start Iteration value like this will push the pattern to the right. Like this: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 - iteration columns 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 - layer 1 red n 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 - layer 2 yellow n n 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 - layer 3 blue n n n 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 - layer 4 green Note that Layer 1 and Layer 4 start to overlap at iteration number 3, so in the UPR, the green covers the red at iterations 3, 6, 9 ... You can see that when you look down column 3 above, where there is a 1 in layer 3 and a 1 in layer 4. Same for column 6 and 9 Another way to look at it is like this: Layer 1 - start at iteration 0, skip 1 and 2, show 3, skip 4 and 5, show 6, skip 7 and 8, ... Layer 2 - start at iteration 1, skip 2 and 3, show 4, skip 5 and 6, show 7, skip 8 and 9, ... Layer 3 - start at iteration 2, skip 3 and 4, show 5, skip 6 and 7, show 8, skip 9 and 10, ... Layer 4 - start at iteration 3, skip 4 and 5, show 6, skip 7 and 8, show 9, skip 10 and 11, ... Hope this helps
someIterations2 {
; Tweaks are OK
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}
someIterations {
; Tweaks are OK
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}
someIterations {
; Tweaks are OK
; I tweaked to maintain the color progression. Thanks for the
; lesson and demo. This has finally made sense to me! LindaD
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}
