What is the method for merging two IFS equations with multiple requirements into a single one?

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One approach to merging two IFS equations with multiple requirements into a single one is to use a "weighted average" technique.

First, transform each IFS equation into the form of a weighted average of multiple linear transformations. Each linear transformation is specified as a matrix and a probability weight.

Next, combine the two sets of linear transformations into a single set by taking a weighted average of the matrices and probability weights. The weights should be chosen so that the requirements of each IFS equation are satisfied in the merged set.

Finally, normalize the probabilities so that they add up to 1, and express the merged set as a single IFS equation. The resulting equation will have the same fractal structure as the original two equations, but with the requirements of both equations taken into account.