Difference between revisions of "Distribution of nonces and hashes"
m (→Histograms: added Wikipedia:Selection bias link) |
m (→Histograms: added headings) |
||
| Line 11: | Line 11: | ||
==Histograms== | ==Histograms== | ||
| + | ===Distribution of Nonces=== | ||
The nonces found are skewed toward 0 because this is a [[Wikipedia:Selection_bias|selection effect]]: most everyone starts searching for nonces starting at 0:<br>[[File:Nonces Histogram.png|histogram of nonces]] | The nonces found are skewed toward 0 because this is a [[Wikipedia:Selection_bias|selection effect]]: most everyone starts searching for nonces starting at 0:<br>[[File:Nonces Histogram.png|histogram of nonces]] | ||
| + | ===Distribution of Hashes=== | ||
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>[[File:Hashes Histogram.png|histogram of hashes]] | Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>[[File:Hashes Histogram.png|histogram of hashes]] | ||
| + | ===2-D Distribution of Nonces & Hashes=== | ||
2-D histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png|Density Plot (log colorscale)]] | 2-D histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png|Density Plot (log colorscale)]] | ||
<br> | <br> | ||
Revision as of 01:02, 14 March 2015
Here we analyze the nonce values and hashes for all the valid blocks in the blockchain:[1]
Contents
Time Evolution
Nonces vs Hashes (y-axis logarithmic, x-axis linear)
This plot readily shows that the distribution of nonces that produce valid hashes is uniform.
Nonces vs Hashes (log-log scale)
.png)
In the animated version of this last plot,[2] you can really visualize the change in the difficulty and even see where the difficulty was decreased.
Histograms
Distribution of Nonces
The nonces found are skewed toward 0 because this is a selection effect: most everyone starts searching for nonces starting at 0:
Distribution of Hashes
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):
2-D Distribution of Nonces & Hashes
2-D histogram of hashes and nonces (logarithmic color scale):.png)
This also illustrates very well that the distribution of nonces is uniform.
References
This page is a stub. Help by expanding it.
