'Widgeon', a variant of 'Ducky Plus'.
'Widgeon' is based on the same principle as 'Ducky Plus': change of the kind of operation during the iteration process. In 'Ducky Plus' there are 3 steps, each with a number of iterations, here in 'Widgeon', the second step consists of only one iteration.
So for each treated pixel the iteration series starts with a certain formula, determined by the parameters in 'Pre iterations' ('Main mode' and 'Main Formula' ).
Then, in the 'Transition Iteration', the value z is reorganized, it becomes another value than the 'normal' orbit should have given. Of course there are many ways to do it, but the possibilities are restricted in this fractal formula by: 4 modi, the transition function, a vector, and one (in modi A, B, and C) or two (in mode D) factors.
After the transition, the iterations go further with the 'Post iterations', with parameters 'End mode', 'End function', 'End vector', and 'End factor'.
Another way to use 'Widgeon' is with button 'Repetativ' enabled. In that case there are no post iterations, only 'pre iterations' (the main iterations), and the 'transition iteration'. Each time the counter has reached the 'transition value' it is reset. When it again has reached the 'transition iteration' the whole operation will repeat, until 'Maximum iterations' has been reached.
In both cases, button 'Repetativ' disabled or enabled, the settings of 'transition iteration' and 'Maximum iterations' are important. Different settings will influence the image considerably.
About the modes:
In 'pre', 'transtion', and 'post' there are 4 modi. Mode A is the original Ducky formula, mode B a variant. For many functions both are identically, but not for cos, acos, acosh, tan, tanh,
cotan, cotanth, sqr, sqrt, log, exp, conj, en recip (uninteresting conversion functions as round, floor, among others are disregarded).
In 'pre' and 'post' all modes are of the same kind. There, in mode C and D only one component of the complex value is a Ducky one, in mode C it is in the imaginary component, in mode D the real one. Their practical usability is somewhat less than that of modes A and B. It's recommended to enable here the 'End log' button.
In the transition iteration modes C and D have other effects. Mode C is a standard function as such, without Ducky properties. Mode D is of the Hokum type: components modulus (= hypotenuse in the right-angled triangle) and argument (one of the sharp angles in the same triangle) are used as a new real and imaginary component.
'Widgeon', a variant of 'Ducky Plus'.
'Widgeon' is based on the same principle as 'Ducky Plus': change of the kind of operation during the iteration process. In 'Ducky Plus' there are 3 steps, each with a number of iterations, here in 'Widgeon', the second step consists of only one iteration.
So for each treated pixel the iteration series starts with a certain formula, determined by the parameters in 'Pre iterations' ('Main mode' and 'Main Formula' ).
Then, in the 'Transition Iteration', the value z is reorganized, it becomes another value than the 'normal' orbit should have given. Of course there are many ways to do it, but the possibilities are restricted in this fractal formula by: 4 modi, the transition function, a vector, and one (in modi A, B, and C) or two (in mode D) factors.
After the transition, the iterations go further with the 'Post iterations', with parameters 'End mode', 'End function', 'End vector', and 'End factor'.
Another way to use 'Widgeon' is with button 'Repetativ' enabled. In that case there are no post iterations, only 'pre iterations' (the main iterations), and the 'transition iteration'. Each time the counter has reached the 'transition value' it is reset. When it again has reached the 'transition iteration' the whole operation will repeat, until 'Maximum iterations' has been reached.
In both cases, button 'Repetativ' disabled or enabled, the settings of 'transition iteration' and 'Maximum iterations' are important. Different settings will influence the image considerably.
About the modes:
In 'pre', 'transtion', and 'post' there are 4 modi. Mode A is the original Ducky formula, mode B a variant. For many functions both are identically, but not for cos, acos, acosh, tan, tanh,
cotan, cotanth, sqr, sqrt, log, exp, conj, en recip (uninteresting conversion functions as round, floor, among others are disregarded).
In 'pre' and 'post' all modes are of the same kind. There, in mode C and D only one component of the complex value is a Ducky one, in mode C it is in the imaginary component, in mode D the real one. Their practical usability is somewhat less than that of modes A and B. It's recommended to enable here the 'End log' button.
In the transition iteration modes C and D have other effects. Mode C is a standard function as such, without Ducky properties. Mode D is of the Hokum type: components modulus (= hypotenuse in the right-angled triangle) and argument (one of the sharp angles in the same triangle) are used as a new real and imaginary component.
