Given
t = time since the shader was applied a full = Full Alpha Ratio a persistent = Persistent Alpha Ratio a offset = a full − a persistent t fade-in = Alpha Fade In Time t full = Alpha Fade In Time + Full Alpha Time t fade-out = Alpha Fade Out Time t end = time at which the shader was removed t freq = Alpha Pulse Frequency {\displaystyle {\begin{aligned}t&={\text{time since the shader was applied}}\\a_{\text{full}}&={\text{Full Alpha Ratio}}\\a_{\text{persistent}}&={\text{Persistent Alpha Ratio}}\\a_{\text{offset}}&=a_{\text{full}}-a_{\text{persistent}}\\t_{\text{fade-in}}&={\text{Alpha Fade In Time}}\\t_{\text{full}}&={\text{Alpha Fade In Time}}+{\text{Full Alpha Time}}\\t_{\text{fade-out}}&={\text{Alpha Fade Out Time}}\\t_{\text{end}}&={\text{time at which the shader was removed}}\\t_{\text{freq}}&={\text{Alpha Pulse Frequency}}\end{aligned}}}
the base alpha is defined as
a base = { a full × t t fade-in , if t fade-in > 0 and t ≤ t fade-in a full , if t fade-in = 0 and t = 0 a full , if t full ≥ t > t fade-in a persistent + ( a offset × t − t full t fade-out ) , if t full + t fade-out > t > t full a persistent × t − t end t fade-out , if t fade-out > 0 and t > t end 0 , if t fade-out = 0 and t ≥ t end {\displaystyle a_{\text{base}}={\begin{cases}a_{\text{full}}\times {\dfrac {t}{t_{\text{fade-in}}}},&{\text{if }}t_{\text{fade-in}}>0{\text{ and }}t\leq t_{\text{fade-in}}\\a_{\text{full}},&{\text{if }}t_{\text{fade-in}}=0{\text{ and }}t=0\\a_{\text{full}},&{\text{if }}t_{\text{full}}\geq t>t_{\text{fade-in}}\\a_{\text{persistent}}+(a_{\text{offset}}\times {\dfrac {t-t_{\text{full}}}{t_{\text{fade-out}}}}),&{\text{if }}t_{\text{full}}+t_{\text{fade-out}}>t>t_{\text{full}}\\a_{\text{persistent}}\times {\dfrac {t-t_{\text{end}}}{t_{\text{fade-out}}}},&{\text{if }}t_{\text{fade-out}}>0{\text{ and }}t>t_{\text{end}}\\0,&{\text{if }}t_{\text{fade-out}}=0{\text{ and }}t\geq t_{\text{end}}\end{cases}}}
and assuming that the alpha pulse uses a sine wave, the current alpha is
a current = a base + s i n ( ) ∗ t freq {\displaystyle a_{\text{current}}=a_{\text{base}}+sin()*t_{\text{freq}}}
