In southern and northern Hungary, we randomly selected 14 sunflower plantations for our drone photography campaign (Supplementary Table 1). The only criterion of selection was that the studied sunflowers should have mature inflorescences. We took 5 photographs of each plantation from heights ranging between 10 and 20 m, depending on the wind speed: at larger wind speeds, lower heights are optimal for the drone. For quantitative analysis, we chose the photographs of best quality.

On July 7, 2020, we performed the first drone photography above a sunflower plantation near the Hungarian town Kiskunhalas (Supplementary Figure 1). The drone (DJI Phantom 3 Standard, field of view = 80^°) captured photographs of mature sunflower inflorescences with its camera (DJI F300C). Using another drone (DJI Phantom 3 Advanced) with another camera (FC300S, field of view = 84^°), in July and August 2021, we conducted a thorough drone photography campaign above 14 different Hungarian sunflower plantations (Figure 1 and Supplementary Figures 2–15). The optical axes of the camera of the drones were parallel to the local gravitational acceleration vector. Supplementary Table 1 summarizes the date, number, location, time, latitude, longitude, height, and camera yaw angle η (measured from the geographical north) of our drone campaigns. In all studied plantations, the hybrid type of the studied sunflowers (H. annuus) was the same: Cortewa (earlier named Pioneer) P64LE25.

At the time of exposure of a photograph, the drone’s navigation system detected the yaw angle η between the drone’s inner reference direction ( = direction of the right side of the photo) and the geographical north (Supplementary Figures 1A,B). In the laboratory, we determined the direction of the normal vector of 200 randomly selected mature sunflower inflorescences in each of the drone photographs taken from 14 different sunflower plantations (Supplementary Table 1). We used a software developed by one of the authors (Ádám Egri), with which one can select a given inflorescence by clicking onto the center of the yellow arc of the flower’s petal series. Then a red circle appeared around the inflorescence with a red pointer (bar), the direction of which could be rotated arbitrarily. Using the computer’s mouse, the evaluator turned this pointer so that its direction became perpendicular to the inflorescence’s surface (Supplementary Figure 1C). Using this procedure, the evaluator estimated the angle β between the inflorescence’s normal vector and the direction of the photograph’s right side (Figure 2). The software registered the value of β and waited for the manual-visual evaluation of the next selected inflorescence. Finally, the azimuth angle α = β + η of the inflorescence’s normal vector measured from the north was obtained (Figure 2).

To explain the phenomenon of the southern orientation of a group of sunflowers shadowed for 5 h both after sunrise and before sunset, we used the computer program developed by Horváth et al. (2020). This software computes the total light energy e per unit area absorbed by a sunflower inflorescence between anthesis (1 July) and senescence (7 September) as a function of the azimuth angle α of its normal vector for the typical cloud conditions of a given region, in our present case for Hungary, where mornings are less cloudy than afternoons. It uses local astronomical data of the celestial motion of the Sun and regional meteorological data of diurnal cloudiness between anthesis and senescence, furthermore the time-dependent elevation angle of mature sunflower heads and the absorption spectra of inflorescences. More details about this computational method can be found in the study by Horváth et al. (2020).

Figure 3 shows the distribution N(α) of the azimuth angle α (measured clockwise from geographical north) of the normal vector of 2,800 ( = 14 × 200) randomly selected mature sunflower inflorescences at locations 1–14 (Supplementary Table 1) determined in the drone photographs (Supplementary Figures 2–15), where N is the number of inflorescences. The average ± SD of the Gaussian curve fitted to the N(α) graph are α_average = 89.5^° ± 42.8^°. α_average practically coincided with the geographical east α_east = 90^°.

Table 1 contains the average azimuth α_average ± SD Δα_SD (measured clockwise from geographical north) of the normal vector of the randomly selected mature sunflower inflorescences at locations 1–14 (Supplementary Figures 16–29 and Supplementary Table 1) determined in the drone photographs of Supplementary Figures 2–15, and the values of the azimuth α_sunrise of local sunrise. According to Table 1, at locations 1–5 and 7–13, the average azimuth angle α_average of sunflower inflorescences changed between 77.6 and 98.3^°, and the minimal and maximal SD were Δα_SD(min) = 24.9^° and Δα_SD(max) = 56.6^°. The minimum and maximum values of the difference Δ_{east–average} = α_east −α_average between α_average and the azimuth α_east = 90^° of geographical east were Δ_{east–average}(min) = 1.1^° and Δ_{east–average}(max) = 12.4^°, respectively. Since in these cases Δ_{east–average} was much smaller than Δα_SD, we conclude that the average azimuth angle α_average of the normal vector of these sunflower inflorescences did not deviate significantly from the geographical eastern direction α_east.

In the studied sunflower plantations, the sun rose at azimuth angles 56.14^° ≤ α_sunrise ≤ 57.55^°, during our drone photography campaigns. According to Table 1, at locations 1–5 and 7–13 the minimum and maximum values of the difference Δ_{average–sunrise} = α_average −α_sunrise between α_average and the azimuth α_sunrise of local sunrise were Δ_{average–sunrise} (min) = 20.94^° and Δ_{average–sunrise} (max) = 40.78^°, respectively. Since in these locations Δ_{average–sunrise} was always much larger than Δ_{east–average}, we conclude that the average azimuth angle α_average of the normal vector of these sunflower inflorescences deviated significantly from the azimuth direction α_sunrise of local sunrise.

However, locations 6 and 14 are exceptions from these trends: At location 6, α_average = 66.4^° ± 51.5^° differed only by Δ_{average–sunrise} = 9.75^° from α_sunrise = 56.65^° and differed by Δ_{east–average} = 23.6^° from α_east = 90^° (Table 1). Here, the SD Δα_SD = 51.5^° was much larger than Δ_{east–average} = 23.6^°, and Δ_{average–sunrise} = 9.75^° was relatively small. From these, we conclude that although the average azimuth of these sunflower inflorescences did not differ significantly from the eastern azimuth α_east = 90^°, it was much closer to the north-eastern azimuth of local sunrise.

At location 14, α_average = 114.4^° ± 39.5^° differed by Δ_{average–sunrise} = 56.85^° from α_sunrise = 57.55^° and differed by Δ_{east–average} = −24.4^° from α_east = 90^° (Table 1). Here, since the SD Δα_SD = 39.5^° was much larger than | Δ_{east–average}| = 24.4^° and Δ_{average–sunrise} = 56.85^° was relatively large, we conclude that the average azimuth of these sunflower inflorescences did not differ significantly from the eastern azimuth α_east = 90^° and differed significantly from the azimuth of local sunrise. Nevertheless, the deviation Δ_{east–average} = −24.4^° of α_average from α_east toward south-east was at least two times larger than at locations 1–5 and 7–13.

The reason for these two last deviations at locations 6 and 14 from the general trends at locations 1–5 and 7–13 positioned on horizontal plane landscapes may be that the sunflower plantations 5 and 14 were in hilly landscapes where the illumination received by sunflower inflorescences more or less differed from that at flat sites.

In sunflower plantation 15 (Sződ 5, Supplementary Table 1), we observed that a group of mature inflorescences faced south rather than east as the majority of sunflowers. For about 5 h after sunrise, this inflorescence group was in the shadow of tree group 1 shown in Figure 1A, while for nearly 5 h prior to sunset it was shadowed by tree group 2 (Figure 1A). Figure 1C shows the distribution of the azimuth angle α (measured clockwise from geographical north) of the normal vector of 100 mature sunflower inflorescences in the white-perimeter rectangle of Figure 1B. The majority of these inflorescences faced practically south (α_average = 181.1^° ≈α_South = 180^°) with SD Δα = ± 20.7^°, and the minimum and maximum of their azimuth were α_min = 63^° and α_max = 219^°, respectively (Figure 1C).

To find a possible reason for the southern orientation of these sunflowers, we computed the total light energy e per unit area absorbed by a sunflower inflorescence between anthesis (1 July) and senescence (7 September) as a function of the azimuth angle α of its normal vector. We used the computer program developed by Horváth et al. (2020) for the typical cloud conditions in Hungary, where mornings are usually less cloudy than afternoons. Since the south-facing sunflowers in Figure 1 were in the shadow of trees both after sunrise and before sunset for approximately 5 h, in our computations we assumed that (i) the model inflorescence was illuminated continuously by diffuse skylight between sunrise and sunset (ii) and it received direct sunlight only in the time interval t_sr + Δt_sr ≤ t ≤ t_ss −Δt_ss, where t_sr and t_ss are the times of sunrise and sunset and Δt_sr and Δt_ss are the periods after sunrise and before sunset, respectively. The computational results for different illumination conditions are shown in Figure 4: