Symmetrical is correct. You have the spacing correct, but that is only one position. For example, if I was to play in the key of Metallica(E), I could do an ascending lick like this, while keeping the finger spacing the same, only changing position on each pair of strings to remain in the same key by only changing the octave. It would be the Aeolian pattern if I was starting on my root note to keep the shred pattern in key while still making it useable to mesh with an E pentatonic. While that is a snippet of a lick and not the entire lick, the rules remain the same for the next part of the progression. The pattern does not change if you change key. It remains the same regardless of key!
e-----------------------------------------------------------------17-19-20–
B-----------------------------------------------------17-19-20--------------
G---------------------------------------14-16-17----------------------------
D--------------------------14-16-17-----------------------------------------
A-------------12-14-15------------------------------------------------------
E-12-14-15------------------------------------------------------------------
Think of the patterns in spacing, octaves and string groups rather than scale names and theory to simplify to make them easy to navigate at high speed. Half step or full step, two strings grouped together, same key and same notes just one octave up or down. It makes things so much easier to think about when playing fast. I regularly find people are so fixated on playing notes and scales to the “rules” of music they bypass the obvious for playing quickly and efficiently.
If I wanted to extend the pattern it would go as follows
First Octave:
e-----------------------------------------------------------------------------
B------------------------------------------------------------------------------
G------------------------------------------------------------------------------
D------------------------------------------------------------------------------
A-------------12-14-15-------------14-15-17--------------15-17-19-
E-12-14-15-------------14-15-17-------------15-17-19--------------
Second Octave:
e-----------------------------------------------------------------------------
B------------------------------------------------------------------------------
G---------------14-16-17-------------16-17-19-------------17-19-21-
D–14-16-17--------------16-17-19-------------17-19-21-------------
A-------------------------------------------------------------------------------
E-------------------------------------------------------------------------------
Third Octave:
e--------------17-19-20--------------19-20-22--------------20-22-24-
B-17-19-20--------------19-20-22--------------20-22-24--------------
G-------------------------------------------------------------------------------
D-------------------------------------------------------------------------------
A-------------------------------------------------------------------------------
E-------------------------------------------------------------------------------
- There are 3 finger spacings - Full step & Half Step - Half Step & Full Step - Full step and Full step
- There are 3 Octaves of the pattern
- There are 3 groups of strings (EA DG Be) the pattern is played across
This keeps a pattern that can be played ridiculously fast and sound awesome, very simple! 3 3 3. Simplfy and fly!