# Alternate Mapping: Orbit Trap Value

The Fractal Science Kit fractal generator Alternate Mapping Orbit Trap Value defines the alternate value in terms of an orbit trap.

The Orbit Trap Value properties pages are:

These pages are as described for Orbit Trap. The only difference is that the Controllers page is omitted and the Properties page is added.

The Properties page supports several properties to control the results.

# General Options

The General Options section holds a single property: Method. Method determines the ordering used when a point is trapped on multiple dwells. Method is set to one of the following values:

• Trap First Point
• Trap Last Point
• Trap Closest Point
• Trap Points Using Dwell Pattern

Remember that during the fractal orbit we keep statistics related to how close the orbit points come to the orbit traps. If more than 1 point within a given orbit is trapped, we need to determine which point's data is retained. Method solves this problem. If Method is Trap First Point, the point with the lowest dwell is selected. If Method is Trap Last Point, the point with the highest dwell is selected. If Method is Trap Closest Point, the point that is closest to the trap is selected. If Method is Trap Points Using Dwell Pattern, the Dwell Pattern section is used to define a permutation of the set of all possible dwell values, and the point whose dwell is closest to the top of the list is selected.

The Method controls the perceived order of the traps. Trap First Point places traps with lower dwells on top of those with higher dwells. Trap Last Point places traps with higher dwells on top of those with lower dwells. Trap Closest Point merges all traps together into a single object. Trap Points Using Dwell Pattern gives finer control over the order and is explained below.

# Dwell Pattern

When Method is Trap Points Using Dwell Pattern, the Dwell Pattern section defines a permutation of the set of all possible dwell values, and the point whose dwell is closest to the top of the list is selected.

Normally, the traps are ordered within an image based on their dwell value. Traps with low dwell values will appear to be above traps with higher dwell values. The properties in this section allow you to define a pattern used to alter the order of the traps. The pattern is an ordered list of integers from 1 to S, where S is the size of the pattern. The list defines the perceived order of traps with dwell values between 1 and S. That is, a trap with dwell value equal to the 1st entry of the pattern would appear above all others. A trap with dwell value equal to the 2nd entry of the pattern would appear just below the 1st, and so on. Next you add S to each of the pattern elements to define an ordering on the next set of S dwell values (dwells S+1 to 2*S). This process continues until the entire set of traps has been reordered.

For example, the pattern [2,1]applied to the dwell values [1,2,3,4,5,6] would result in the list [2,1,4,3,6,5], effectively reversing every pair of values. The pattern [1,3,2,4] applied to the dwell values [1,2,3,4,5,6,7,8] would result in the list [1,3,2,4,5,7,6,8].

The Pattern property is set to one of the following values:

• P1: [ 1,2,3,4 ] (size N)
• P2: [ 1,5,2,6,3,7,4,8 ] (size 2N)
• P3: [ 5,1,6,2,7,3,8,4 ] (size 2N)
• P4: [ 1,8,2,7,3,6,4,5 ] (size 2N)
• P5: [ 8,1,7,2,6,3,5,4 ] (size 2N)
• P6: [ 1,3,5,7,2,4,6,8 ] (size 2N)

These are the 6 supported patterns. The property N controls the size of the pattern. The size is either N (for pattern P1) or 2N for the rest of the patterns. The pattern values given in the Pattern property text correspond to N equal to 4. As you increase N, the complexity of the image increases as more of the higher dwells become visible. N should be an integer between 2 and 16 inclusive.

The properties Rotate, Reverse Pattern, and Reverse Direction are used to alter the selected pattern. Rotate shifts the pattern to the left by Rotate elements. Numbers that fall off the left side of the pattern are added back into the pattern on the right. Rotate is an integer between 0 and S-1, where S is the size of the pattern (2N in most cases). Reverse Pattern reverses the pattern. Reverse Pattern is checked by default so that the larger traps are pushed down in the order and the smaller traps are displayed on top yielding a more interesting image. Reverse Direction applies the pattern starting with the last dwell and ending with the first dwell.

# Index Map

The alternate point's Index is set to the value given by Index Map. Index Map is one of the following:

• Combined Index
• Trap Index
• Trap Delta
• Trap Dwell
• Trap Count

Trap Index equates to trappedPoint.Index. Trap Delta equates to trappedPoint.Delta. Trap Dwell equates to the trapped point's dwell value. Trap Count is the number of traps that trapped the point.

Unlike these other settings, Combined Index is not useful for coloring. However, since the Combined Index combines the other index values to form a unique value and Index is used by Solid Guessing to determine if 2 samples are equal, differences in the index values will cause the samples to be seen as not equal, which will improve the visible results of Solid Guessing. So the recommendation is to use Combined Index for Index Map unless you need to use the index for coloring.

The alternate point's Angle is set to the trapped point's angle (trappedPoint.Angle).

# Orbit Generation

The Orbit Generation section defines 3 properties: Min Dwell, Max Dwell, and Mod Dwell. These values control the set of orbit points that are considered when processing the orbit. Min Dwell is the 1st dwell to check. Max Dwell is the last dwell to check. Mod Dwell - 1 is the number of dwells to skip between checks. That is, a dwell is processed if the dwell is between MinDwell and MaxDwell inclusive, and (dwell - MinDwell) % ModDwell = 0.