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Graph Digitizer

RayTomes — Sun, 30 Aug 2026 07:52:18 +0000

Quite often I find graphs published in articles but I can not find the data that the graph is based on. It can be very frustrating. So I made this app to allow the graphic to be dropped into it and after a few clicks on the scales and such it gives you a CSV file of the data in the graph. Here are the steps to follow:

Copy the code below into your browser (or save and click to load).
Load the image by browsing to it.
Calibrate the x axis (usually time) by clicking each of an early and late date/time and specifying the value at that point.
If the y axis is on a log scale click that button.
Calibrate the y axis by clicking each of a low vale and a high value on the scale and typing in those values.
Give the series a name.
Select the colour with the cross hairs. Can be delicate for thin lines but it shows what you selected. If you miss you can try again.
Give it the lower left and upper right corners that the graph stays inside. Make sure that there are no other things of that colour in that area or they will get digitized too.
Press extract curve.
Copy the resulting CSV file which has the co-ordinates of all the x,y points along the graph.
Go paste it somewhere useful.

Thanks Claude for your help.

Graph Digitizer

Load a chart image, calibrate its axes against two known reference points on each, sample the curve's color, then extract a dense table of coordinate pairs. Everything runs locally in this page.

Load image

Drop a chart image, or browse for one.

Drop image here, or click to choose a file

Calibrate X axis

Click two points on the X axis whose values you know (e.g. two gridline ticks), entering the value after each click.

Log scale on X

Calibrate Y axis

Same idea, on the Y axis.

Log scale on Y

Trace a curve

Name the series, then click directly on the curve in the image to sample its color. Adjust tolerance if it misses spots or catches noise.

Series name

Color match tolerance: 45

Not set — will scan the whole image. Set this if legend text, axis labels, or anything else shares the curve's color.

Series extracted

None yet

Output

X axis label

Resample to even X steps

x	y

Combine series into one file

Kotov's Method App

RayTomes — Sun, 30 Aug 2026 07:26:06 +0000

The following is an app for calculating Kotov' Method for communality of a set of values. You just load it into a browser and then past or type in the list of values to the window, select the range over which you want the spectrum and press compute spectrum. It is preloaded with the Planets distance from the Sun for you to see the sort of results that you can expect.

In my research this is a method that I have used very extensively with great results. When I ran this on the radius of black holes recently (there is much better data now than when I wrote on it in my book) it showed that exactly the same two big peaks occurred in black holes as in the solar system. Quite clearly the same waves pervade the entire Universe (as black holes are at the centre of most or all galaxies).

I cannot recommend this technique too highly. Thank you Kotov who sadly died late last year. He also discovered the 160 minute cycle in the Sun, which wikipedia erroneously says is not real. He showed that the 160 minute cycle is present in many classes of objects - binaries, asteroid rotations, etc as well as the planets.





Kotov's Method v2 — Black Hole Event Horizon Radii





Kotov's Method v2
Click any row in the peak table below to highlight that point on the plot and see the per-point fit breakdown.


  
    
      Input values — one per line: value, optional ", weight"
      0.387, Mercury
0.723, Venus
1.000, Earth
1.524, Mars
5.203, Jupiter
9.537, Saturn
19.191, Uranus
30.069, Neptune
39.482, Pluto (dwarf planet)
    
    
      Range min
      Range max
    
    
      Coarse step size (% per step, log scale)
      
      
    
    
      Error exponent
      
         1
         2
         3
      
    
    
      
    
  

  
    
      Commensurability spectrum
      
      Trial quantum value (log scale)
    
    
      Strongest peaks (refined) — click a row to highlight on the plot
      
         Strongest first
         Numerical order
      
      
        # Trial value Relative strength
        
      
    
    
      Fit breakdown
      
        Input value Ratio Nearest integer Deviation

How Accurately Can We Measure Cycle Periods?

RayTomes — Sat, 25 Jul 2026 04:44:39 +0000

How Accurately Can We Measure Cycle Periods?

When a piece of cycles research reports a period like "26.65 million years" or "3.41 years," there's an obvious follow-up question that too often goes unanswered: how precisely is that actually known? A number without a stated precision invites two opposite mistakes — dismissing a real match because it "isn't exact," or accepting a false match because it "looks close." Both are avoidable with a simple rule.

The rule

Accuracy = cycle period ÷ (10 × number of full cycles present in the data)

The "number of full cycles present" is just the total length of the data divided by the candidate period. So a longer data span, or a shorter candidate period, both mean more repeats of the cycle are on record — and the more repeats you have, the tighter the accuracy the rule assigns.

A necessary condition: the method has to allow a fractional number of cycles

The rule only holds for spectral methods that let a trial period fit a non-integer number of cycles into the data window — techniques in the least-squares spectral analysis family, which search continuously across frequency rather than only at fixed grid points.

CATS software does do fractional numbers of cycles in the data, down to 0.01 variations which is more than adequate for getting within 0.1 cycles.

An ordinary DFT (or the FFT that computes it efficiently) doesn't have this freedom: it's restricted to a fixed harmonic grid, which effectively forces a whole number of cycles to fit exactly into the data span. That constraint alone costs a factor of about ten in the achievable precision. So the rule above assumes a fitting method that isn't hamstrung this way — with a plain FFT, the same data yields roughly ten times the uncertainty.

Why it works

The intuition is straightforward: each time a cycle completes another full repeat within the data, that's another independent confirmation of exactly where its peaks and troughs fall. Fitting the centre of a known, clean waveform shape against many repeats pins down its period far more tightly than a single repeat could, because the errors in locating each individual peak partly cancel out across the whole set rather than adding up.

The factor of 10 in the rule isn't a guess — it was established empirically, by testing the method on monthly commodity price data containing cycles of known, exactly-verifiable length: 12, 6, 4, 3, and 2.4 months, all arising directly from the calendar seasons. Because the true periods in that test case were already certain, the actual precision the method achieved could be measured directly against them, and a consistent ×10 improvement over the naive resolution limit held up.

Applied to the recent factor-analysis results from 281 years of spliced European commodity price data, the rule reproduces the exact stated precision for each cycle found:

Cycle (years)	Cycles present (281 ÷ period)	Rule's stated accuracy
2.953	95.2	±0.003
3.411	82.4	±0.004
7.23	38.9	±0.02
10.96	25.6	±0.04

Notice the pattern: shorter cycles, with many more repeats fitting into the same data span, get pinned down far more tightly than longer cycles with only a few repeats — exactly what the rule predicts.

Why the distinction matters in practice

Applying the rule honestly changes which apparent "matches" between a found cycle and a known reference cycle actually hold up.

A found period of 10.96 years, with a rule-derived accuracy of ±0.04, is a genuine match to the roughly 11-year sunspot cycle — the gap between them is well inside the stated uncertainty.

But a found period of 3.411 years, with a much tighter accuracy of ±0.004 owing to its many repeats in the data, turns out not to be a genuine match to the well-known 3.389-year (40-month) stock market cycle — the gap between them, though small in absolute terms, is more than five times the stated precision.

This is the central, sometimes uncomfortable lesson: a number that "looks close" is not the same as a number that matches within its properly calculated precision.

Appendix: how this relates to the uncertainty principle

The rule above answers a different question from the one usually raised when "uncertainty" comes up in cycles work, and it's worth being precise about the difference.

There are really two separate questions:

How close together can two real periods be before we can no longer tell them apart at all? This is a hard limit set purely by how much data you have.
Given that a single, clean cycle really is there, how precisely can we pin down its exact value? This is a much softer limit, set by the quality of the fit — and it's what the rule above answers.

The first question is where a version of Heisenberg's uncertainty principle comes in. It can be rearranged from its usual energy-time form (ΔE·Δt ≥ a fixed constant) into a statement about cycles: (time uncertainty) × (period uncertainty) is bounded, where the time uncertainty is simply the length of the data. This is the classical time-bandwidth product (the Gabor limit) that falls out of the same Fourier mathematics behind the quantum relation — not because it's literally quantum mechanics, but because both are consequences of the same fact about Fourier-conjugate pairs. Converted to a period uncertainty, it becomes the standard Rayleigh frequency-resolution criterion from spectroscopy and signal processing: period² ÷ data-span — the naive baseline that the rule above improves on by roughly a factor of 10.

The reason the two questions have different answers is the same reason a telescope's diffraction limit sets how close two stars can appear before blurring into one, while the position of a single isolated star can still be measured to a small fraction of that same diffraction width, given a clean enough signal. The Fourier/Rayleigh limit sets the width you can't beat without more data; the ×10 rule is the empirically-measured centroiding gain available within that width when a single clean cycle is being fitted rather than two cycles being separated. Both trace back to the same underlying relation — one from the physics-textbook side, one rediscovered independently from the data-analysis side.

Source / publisher: Wikipedia
URL type: WWW
Credits: Wikipedia
URL: https://en.wikipedia.org/wiki/Electromagnetic_spectroscopy