Saturday, December 30, 2023
Wednesday, December 27, 2023
Flush fill cap
Slightly recessed |
This flush fill cap has skinny "fingers". Installation slightly below sidewalk level keeps this oil tank cap from being tread upon by wayward soles. That allows the non-ferrous metal to acquire a slight patina.
Friday, December 22, 2023
Double vee gas
Tuesday, December 19, 2023
BPM worn
Wednesday, December 13, 2023
Smoke plume
Thursday, December 7, 2023
Two panes
Saturday, December 2, 2023
Monday, November 27, 2023
East and west contrails
Heading east |
The contrail from a twin engine jet airliner heading east is colored by the setting sun.
Monday, November 20, 2023
Tree chomping
Teeth marks of the chomper |
A closer look at the splintered end of the toppled tree. Look at those teeth marks! Each chomp takes out a piece of tree that is two to three inch long and about one-half inch thick.
Thursday, November 9, 2023
Falling tulip tree
Tulip tree in autumn |
Sunlight from the setting sun makes the already bright fall foliage of this Liriodendron tulipifera (tulip tree) even more colorful.
Sunday, November 5, 2023
Color on the bank
Tuesday, October 31, 2023
River seen
Sunday, October 22, 2023
Caution - do not step on cracks
Tuesday, October 17, 2023
Cocooning for winter
Tuesday, October 10, 2023
Squash the spotted
Tuesday, October 3, 2023
Sun dog in the clouds
Saturday, September 30, 2023
Contrail in the sky, too
Monday, September 18, 2023
Contrail in the sky
Wednesday, September 13, 2023
Switch in place
Friday, September 8, 2023
Silver twist
Monday, August 28, 2023
A note for Mom
Monday, August 21, 2023
A flute for you
Tuesday, August 8, 2023
Rays on the water
Wednesday, August 2, 2023
Hot day clouds
Monday, July 24, 2023
Track in the rain
Tuesday, July 18, 2023
Waclaw Szpakowski - Rhythmic Lines (01)
"A10" (1924) - Waclaw Szpakowski |
Szpakowski transformed many of these "doodles" from his notebooks into precisely drawn line figures. He called these "Linie rytmiczne" [Rhythmic Lines]. He drew these using a Graphos, a technical drawing pen made by Pelikan. The result was a uniform, unmodulated, one millimeter thick line. The gap between neighboring line segments would be four millimeters. In effect, these were squares. He often used 4x4 squares graphing paper. Szpakowski created some of his line figures from repeated mirroring and flipping of horizontal and vertical portions of his design. A look at these figures shows they could be fractals, maybe resembling the Sierpinski Triangle, or Greek key patterns, flat sheet heating elements, folded antennas, Hilbert space-filling curves, or, musical / sound waveforms?
Szpakowski called these figures "rhythmical lines". Tracing the lines can lead to a meditative quality to that experience. In an interview, artist Anna Szpakowska-Kujawska, his daughter, says they should be called "linie psychiczne" (lines from the psyche, lines of the psyche) as they often reflected his moods and feelings when he drew them. These figures have a devoted following and have a home on the web (see selected links below).
R1 = row 1 = uppermost row
Rn = row n = bottommost row
C = number of columns = x-axis
C1 = column 1 = leftmost column
Cn = column n = rightmost column
A = area = R x C = number of squares in figure
slope = delta y-axis / delta x-axis = R / C
P = perimeter = 2 x R + 2 x C
LL = line length = number of line segments (each segment is one square in length)
SOH CAH TOA
tan = opposite / adjacent
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
slope formula
m = (y2 – y1)/(x2 – x1)
y = mx + b
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix.
Coloring the figure makes it easier to see the structure and patterns within figure A10. On the left side, we can see the initial form A. The horizontal flip of this form is to the right of it. The resulting pattern (the form A plus the horizontally flipped A) makes one wavelength that is repeated; in A10 it repeats three times. The initial form A appears six times, three times as itself, and three times as its horizontally flipped image.
A10 - wavelength equals form A plus horizontal flip of form A |
A10 - graph of yellow and pink colors by row |
This reveals a distribution pattern. The values of rows 1 to 13 are repeated in rows 13 to 25 but with a horizontal flip of the rows 13 to 25. For example, row 3 is 33 yellow and 45 pink; the corresponding row 23 is 45 yellow and 33 pink, and so on. This distribution can also be presented as:
A10 - graph of yellow and pink colors per row |
This second graph reveals the oscillation of the colors on each row. looking across the columns within the waveform. In rows 3 through 11 and rows 15 to 23, there always 33 columns of one color and 45 columns of the other color, the color depending on the row. In the middle, we can see that there is an equal number (39) of both colors. We also note that there are an equal number (975) of yellow and pink squares.
A10 - graph of yellow and pink colors by columns |
A10 - graph of yellow and pink colors by columns |
This closer look at the figures created by Waclaw Szpakowski reveals that not only are his figures composed of repeating waveforms but within these waveforms are also many smaller forms; together, these create the greater waveform. There are also symmetries and regular oscillations. This gives us a clearer insight into what he was thinking as he created these figures.
More about the times in the life of Waclaw Szpakowski can be found at several web pages; these include:
https://waclawszpakowski.pl/ Website dedicated to the work of Wacław Szpakowski
https://culture.pl/en/artist/waclaw-szpakowski Wacław Szpakowski - Biography
Friday, July 14, 2023
Laughing clowns
Monday, July 10, 2023
Thursday, June 29, 2023
I spin for you
Wednesday, June 21, 2023
White on beige
Wednesday, June 14, 2023
South End Office
Thursday, June 1, 2023
Witer water cover