VMI Research

Visual Math Institute

Ralph Abraham, Director

Electric Sheep Data

Preliminary Results

From flock 165 of March -- October, 2004, with 6,380 sheep.

Table of Flames This is a 3 by 3 tableau of exemplary flames from flock 165 Histogram 01 Number of sheep vs rating Scatterplot 01 Rating vs fractal dimension NOTE: Fractal dimensions are subject to jitter (less than 1%): This is a 3 by 3 tableau of exemplary flames from flock 165
Histogram 01 Number of sheep vs rating Scatterplot 01 Rating vs fractal dimension NOTE: Fractal dimensions are subject to jitter (less than 1%): Number of sheep vs rating
Scatterplot 01 Rating vs fractal dimension NOTE: Fractal dimensions are subject to jitter (less than 1%): Rating vs fractal dimension; NOTE: Fractal dimensions are subject to jitter (less than 1%)

From flock 165 with the 684 highest ranking sheep only.

Histogram 02, Freq vs Rating, 21 April 2005 Number of sheep (labelled "frequency") receiving given rating (mislabelled as "# Votes") i.e., 149 sheep received rating 2, 119 received rating 3, etc. Histogram 03, Freq vs Dimension Number of sheep in fractal dimension ranges; i.e., 125 sheep have fractal dimension between 1.6 and 1.69, 37 sheep have fractal dimension between 1.3 and 1.39, etc. Scatterplot 02, Rating vs Dimension Rating vs fractal dimension (similar to Scatterplot 01 above but with sheep receiving votes of -1, 0, and 1 omitted). Histogram, Freq vs Dimension, 06 May 2005 Number of sheep ("count") vs fractal dimension More accurate than Histogram 03 Most popular dimension is 1.56 Histogram 2D, Freq vs Rating and Dimension 06 May 2005 Number of sheep ("count") vs max rating and fractal dimension: Number of sheep (labelled "frequency") receiving given rating (mislabelled as "# Votes"); i.e., 149 sheep received rating 2, 119 received rating 3, etc.
Histogram 03, Freq vs Dimension Number of sheep in fractal dimension ranges; i.e., 125 sheep have fractal dimension between 1.6 and 1.69, 37 sheep have fractal dimension between 1.3 and 1.39, etc. Scatterplot 02, Rating vs Dimension Rating vs fractal dimension (similar to Scatterplot 01 above but with sheep receiving votes of -1, 0, and 1 omitted). Histogram, Freq vs Dimension, 06 May 2005 Number of sheep ("count") vs fractal dimension More accurate than Histogram 03 Most popular dimension is 1.56 Histogram 2D, Freq vs Rating and Dimension 06 May 2005 Number of sheep ("count") vs max rating and fractal dimension: Number of sheep in fractal dimension ranges;; i.e., 125 sheep have fractal dimension between 1.6 and 1.69,; 37 sheep have fractal dimension between 1.3 and 1.39, etc.
Scatterplot 02, Rating vs Dimension Rating vs fractal dimension (similar to Scatterplot 01 above but with sheep receiving votes of -1, 0, and 1 omitted). Histogram, Freq vs Dimension, 06 May 2005 Number of sheep ("count") vs fractal dimension More accurate than Histogram 03 Most popular dimension is 1.56 Histogram 2D, Freq vs Rating and Dimension 06 May 2005 Number of sheep ("count") vs max rating and fractal dimension: Rating vs fractal dimension (similar to Scatterplot 01 above but with sheep receiving votes of -1, 0, and 1 omitted).
Histogram, Freq vs Dimension, 06 May 2005 Number of sheep ("count") vs fractal dimension More accurate than Histogram 03 Most popular dimension is 1.56 Histogram 2D, Freq vs Rating and Dimension 06 May 2005 Number of sheep ("count") vs max rating and fractal dimension: Number of sheep ("count") vs fractal dimension; More accurate than Histogram 03; Most popular dimension is 1.56
Histogram 2D, Freq vs Rating and Dimension 06 May 2005 Number of sheep ("count") vs max rating and fractal dimension: Number of sheep ("count") vs max rating and fractal dimension

Time Series Data

Here, the reduced data for flock 165 (684 sheep) are here chunked into 11 chunks
of about two-week duration. The results are displayed various way:
relative and cumulative counts, average, and mode (most popular)
dimensions computed in each chunk, T1,..., T11.

Count vs dim and time, 1 2D histogram of CUMULATIVE count vs dim and time Wire-frame display Count vs dim and time, 2 2D histogram of CUMULATIVE count vs dim and time Color bar display Favorite dim vs time Graph of average and modal dim vs time Animated histogram we start of with a 1D histogram for each time chunk and then compute the relative % within a given range; for example, in T=1, approx. 23% of the sheep had dim around 1.7. then the 1D histograms, count (as percent of the 684 sheep)) vs dim, for each chunk, animated in sequential time are combined into an 11 frame animated GIF, 72 KB.: 2D histogram of CUMULATIVE count vs dim and time; Wire-frame display
Count vs dim and time, 2 2D histogram of CUMULATIVE count vs dim and time Color bar display Favorite dim vs time Graph of average and modal dim vs time Animated histogram we start of with a 1D histogram for each time chunk and then compute the relative % within a given range; for example, in T=1, approx. 23% of the sheep had dim around 1.7. then the 1D histograms, count (as percent of the 684 sheep)) vs dim, for each chunk, animated in sequential time are combined into an 11 frame animated GIF, 72 KB.: 2D histogram of CUMULATIVE count vs dim and time; Color bar display
Favorite dim vs time Graph of average and modal dim vs time Animated histogram we start of with a 1D histogram for each time chunk and then compute the relative % within a given range; for example, in T=1, approx. 23% of the sheep had dim around 1.7. then the 1D histograms, count (as percent of the 684 sheep)) vs dim, for each chunk, animated in sequential time are combined into an 11 frame animated GIF, 72 KB.: Graph of average and modal dim vs time
Animated histogram we start of with a 1D histogram for each time chunk and then compute the relative % within a given range; for example, in T=1, approx. 23% of the sheep had dim around 1.7. then the 1D histograms, count (as percent of the 684 sheep)) vs dim, for each chunk, animated in sequential time are combined into an 11 frame animated GIF, 72 KB.: we start of with a 1D histogram for each time chunk
and then compute the relative % within a given range;
for example, in T=1, approx. 23% of the sheep had
dim around 1.7.
then the 1D histograms, count (as percent of the 684 sheep))
vs dim, for each chunk, animated in sequential time
are combined into an 11 frame animated GIF, 72 KB.; then the 1D histograms, count (as percent of the 684 sheep))
vs dim, for each chunk, animated in sequential time
are combined into an 11 frame animated GIF, 72 KB.

Revised 20 May 2005 by Ralph Abraham