S&P 500 Logarithmic Chart For ThinkOrSwim

[RandyP]

With these inputs:
SPY Monthly Max Available
startDate 19940103
rate .0065 (happens to be close to 8% annual return)

You get these charts. One chart is log price axis, the other is non-log. The log chart is nearly identical to the Wikipedia S&P 500, best-fit logarithmic chart:
https://en.wikipedia.org/wiki/File:S&P_500_Index_Logarithmic_Chart_through_Jan_2021.svg

wiki states:
While S&P 500 data to linear plot scale is good for analysis of a span of 2 or 3 years, beyond that a logarithmic S&P 500 chart is best. This is because it gives the same Y or vertical displacement for a certain percentage move up or down regardless of date.

IMPORTANT:
Please note that this script does not calculate a best-fit line or curve (that's complicate math). The math here draws a curve based on a simple, non-linear equation with user inputted values. When the right values for the variables are chosen, the curve HAPPENS to match up with SPY for the past three decades.

#diaglinefromdate

def na = double.nan;
def bn = barnumber();
def date = getyyyymmdd();

input startDate = 20240305;
input price = close;
input rate = 0.005;

def y = if bn == 1 then 0
 else if startDate == date then price
 else if y[1] > 0 and !isnan(close) then y[1] + (y[1] * rate)
 else 0;

plot z = if y > 0 then y else na;

#addverticalline(startDate == date, "-");
#

Thank you To @halcyonguy code from here:
https://usethinkscript.com/threads/plot-curve-recursion-from-anchor-date.18616/
I tweaked a couple of things:
- modified the y calculation on the line starting "else if y[1] . . . . . ."
-changed a couple of variable names/input values