English: S&P 500 Index Logarithmic Chart's Interesting Features

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 because it gives the same Y or vertical displacement for a certain percentage move up or down regardless of date. Moreover, a fixed compound interest percentage gain plots as a straight line which is very useful as the human eye is very good at judging and comparing data positions above and below a straight line (versus the linear plot's exponential curve for same).
The given chart with Y axis logarithmic $ values was generated using Excel. There is an upper cluster of lines in USD $ as published WITH INFLATION, and a lower cluster of lines INFLATION SUBTRACTED in 1950 $, (inflation data from: https://inflationdata.com/Inflation/Inflation_Rate/CurrentInflation.asp?reloaded=true )
The upper cluster has two roughly parallel curvy plots using S&P 500 monthly $ MAXIMUM values for the upper line and $ MINIMUM values for the lower line (data from Finance Yahoo history: https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC ) and the X axis shows dates 1945 to latest plus some years, with analysis of all months from 1/1950 to latest on chart. The upper cluster also has two STRAIGHT parallel lines, the upper line Best Fit Upper or BFU, and lower line Best Fit Lower or BFL. The two straight lines represent one line with thickness, or separation, from a calculated average of the monthly S&P 500 Max-Min span or long-term average monthly fluctuation, approximately 6.5% value see chart legend.
Fitting the Straight Lines to the S&P 500 plot was by accumulation of excess (using Logs) that is for increasing months adding positive differences for the upper plot above the upper Straight Line and negative differences for the lower plot below the lower Straight Line, giving an accumulating area value starting 1950 to latest year on chart. Where the S&P 500 plot versus straight line has a ‘very low absolute value’ of preceding area accumulation this is a Best Fit place month marked by a logic HIGH on the FIT chart shown at the bottom of the graph as $11, Not FIT LOW as $10. The Best Fit was found by retrying different % slopes with different $ starting points and observing the Fit chart and sum of Fit months. The parameters giving the largest sum of Best Fit months was plotted with a ‘very low absolute value’ that gives some plot detail. The Jan 2023 chart Best Fit of 7.7%, is an updated fit versus 2021 plot’s 7.5%.
The lower cluster also has two roughly parallel S&P 500 curvy plots taken from the upper cluster S&P 500 plots but are LESS Inflation so look different and have less slope. The lower cluster has two additional parallel lines derived from the straight lines BFU and BFL but also without inflation so are now no longer straight, also start in 1/1950. The lower cluster includes a straight line, added for guide and information, of a compound interest % per annum based in 1990, value see chart legend.
US Government Debt plots WITH and WITHOUT inflation and GDP plot are added to show percentage slope relative to S&P 500, both based in January 1980 but the Y scale is arbitrary so NOT valid $. The plot start base in 1980 is not the S&P 500 value so that the plot, which follows the S&P 500 and Straight Lines closely, isn’t over the top of them. Gold is included as an interesting aside and $ per ounce Y scale is valid.

Logarithmic Chart's Interesting Interpretations
The upper cluster S&P 500 plots including inflation follow a straight line percentage gain in the long term; therefore inflation somehow evens out the ups (over-performance) and downs (under-performance) of the S&P 500 without inflation.
A Moving Average chart, not used here, is inherently delayed from the source chart and difficult to use for prediction. The fitted Straight Line assumes a straight line is correct long term and predicts that a current period of S&P 500 highly deviated from it will eventually correct with a period of opposite accumulated area deviation. This postulate is based on only 75 years of data likely insufficient except for large deviations.
It is interesting to note that the 1954-74 post-war 20 year growth period above the straight line is later balanced by the 1974-87, 13 years, below the straight line. Also, the Internet Bubble from 1995, peaking way-above the line at 2000, is followed by dips, 2002 and especially 2009, below the straight line, not returning to the line until 2018.
Interestingly, the WITHOUT inflation S&P 500 plot best shows its Index cycles. 1954 to 1987 was 33 years of boom-overshoot (peak 1969), then deep fallback, before recovery back to the overshoot peak 1987. Another index cycle of 23 years 1995 to 2018 is shown: 1995 to 2000 boom overshoot-peak, fall back to 2009, then recovery back to the overshoot peak in 2015/8. 2015/8 onwards maybe a new cycle.
Interestingly, the increasing US National Debt % slope closely matches the S&P 500 % slope. Slope acceleration in Debt seem to precede S&P 500 slope acceleration by a 6 to 8 years. Data from: http://www.treasurydirect.gov/govt/reports/pd/histdebt/histdebt_histo5.htm
The GDP graph % slope greatly underperforms the S&P 500 % slope. Data from: http://www.bea.gov/national/index.htm#gdp

Gold’s $ per ounce unusual relative % performance can also be compared to the S&P 500 % slope. Data from: https://www.usagold.com/reference/prices/goldhistory.php