Olapol mapping
There's a new version of mapping 'Olapol' on the UF Formula Database (ea.uxf).
When using old upr's, which made use of the original version 1.00, you'll don't have problems.
These upr's will work automatically with this new version.
First we see a question: "Addition or Single?". These options both use some basic mapping formulas.
'Addition' is the same as 'Olapol' vs.1.01.
At every addition one of 3 available formulas is selected in a random manner.
It makes little sense to increase the number (in "# of additions) to high values.
Relatively low values already give interesting images.
The randomness can be adjusted by changing the parameter 'seed'. (Default it is 123456789.)
'Threshold' and 'Ceiling' are default on 1/3 and 2/3.
So the probability of the selection of a formula from the three available formulas for each subsequent addition = 1/3.
By varying these parameters, you can change the probability distribution.
'Single' is the option for choosing only one formula.
Here there are two possibilities: one way, the default setting, and "the other way".
In the default setting we can select with parameter 'Key' from five available formulas.
Nos #0, #2 and #4 show distorted pictures as we already know from vs.1.00, and also from IFS Apollo (reb.uxl).
Nos #1 and #3 are new, they provide much stronger distorted images.
'The other way' gives two formulas: A and B.
Both consist of two components, controlled by the complex parameter 'Balance'.
In the second part, "Other parameters" are two possible paths: 'Geometric mode enabled or disabled'.
Default this parameter is disabled. We then see two parameters, 1 and 2, affecting the shape of the image.
If the 'Geometric' is enabled, we see only one parameter: 'angle'.
It is a vertex of a fictitious right triangle. Also this angle has a large influence on the shape of the image.
Finally we see a number of general complex parameters which also have influence on the image.
They always work, regardless of the position of the modes adjusted:
- Parameter #3
- Center (which is related to the origin)
- Scale. This is not a scaling factor that acts as a 'zoom'. Even with this parameter 'scale' the image can be distorted.
Notes.
- The same kind of mapping can be found as 'Pallas' in ea.uxf, a further development of 'Olapol' with more direct control on all parameters.
- Olapol and Pallas are especially useful for Ducky and related fractal formulas.
- In the the original 'Apollo' en in the former version of 'Olapol' we see parameter 'Number of Iterations', it has been changed into 'Number of additions',
because there are no iterations, only additions. There (mode 'Addition)', the procedure is like a fruit machine,
a very simple one, with only 3 possibilities, corresponding with the 3 formulas in the loop.
For instance, #1000 gives the same image as #4.
In fact, with the given seed of 123456789, as we did here, the 3 different images are already reached after 5 pseudo-iterations,
Nos #1, 2 and 3 are identical, #4 and #5 provide the other two.
With thanks to Ron Barnett who gave kind permission to modify his original Apollo mapping.
Olapol mapping
There's a new version of mapping 'Olapol' on the UF Formula Database (ea.uxf).
When using old upr's, which made use of the original version 1.00, you'll don't have problems.
These upr's will work automatically with this new version.
First we see a question: "Addition or Single?". These options both use some basic mapping formulas.
'Addition' is the same as 'Olapol' vs.1.01.
At every addition one of 3 available formulas is selected in a random manner.
It makes little sense to increase the number (in "# of additions) to high values.
Relatively low values already give interesting images.
The randomness can be adjusted by changing the parameter 'seed'. (Default it is 123456789.)
'Threshold' and 'Ceiling' are default on 1/3 and 2/3.
So the probability of the selection of a formula from the three available formulas for each subsequent addition = 1/3.
By varying these parameters, you can change the probability distribution.
'Single' is the option for choosing only one formula.
Here there are two possibilities: one way, the default setting, and "the other way".
In the default setting we can select with parameter 'Key' from five available formulas.
Nos #0, #2 and #4 show distorted pictures as we already know from vs.1.00, and also from IFS Apollo (reb.uxl).
Nos #1 and #3 are new, they provide much stronger distorted images.
'The other way' gives two formulas: A and B.
Both consist of two components, controlled by the complex parameter 'Balance'.
In the second part, "Other parameters" are two possible paths: 'Geometric mode enabled or disabled'.
Default this parameter is disabled. We then see two parameters, 1 and 2, affecting the shape of the image.
If the 'Geometric' is enabled, we see only one parameter: 'angle'.
It is a vertex of a fictitious right triangle. Also this angle has a large influence on the shape of the image.
Finally we see a number of general complex parameters which also have influence on the image.
They always work, regardless of the position of the modes adjusted:
- Parameter #3
- Center (which is related to the origin)
- Scale. This is not a scaling factor that acts as a 'zoom'. Even with this parameter 'scale' the image can be distorted.
Notes.
1. The same kind of mapping can be found as 'Pallas' in ea.uxf, a further development of 'Olapol' with more direct control on all parameters.
2. Olapol and Pallas are especially useful for Ducky and related fractal formulas.
3. In the the original 'Apollo' en in the former version of 'Olapol' we see parameter 'Number of Iterations', it has been changed into 'Number of additions',
because there are no iterations, only additions. There (mode 'Addition)', the procedure is like a fruit machine,
a very simple one, with only 3 possibilities, corresponding with the 3 formulas in the loop.
For instance, #1000 gives the same image as #4.
In fact, with the given seed of 123456789, as we did here, the 3 different images are already reached after 5 pseudo-iterations,
Nos #1, 2 and 3 are identical, #4 and #5 provide the other two.
With thanks to Ron Barnett who gave kind permission to modify his original Apollo mapping.
