What is the WorldBiG binary grid?
WorldBiG is a method of differentiating the area of land and on this basis drawing conclusions about the area.
We are trying to develop the concept of a binary grid for analysis and graphic presentation of surface data.
Our aim is to do this simply and practically. So that the WorldBiG grid can be used by everyone, regardless of their field of study and type.
We are convinced that the method of using the surface 'differentiation' grid can help not only botanists, but also doctors, sociologists, foresters, geologists, archaeologists, treasure hunters and so on. It will help in analyses of time trends of pollination of cities or municipalities and other economic analyses.
Short on the World Binary Grid (WorldBiG)
The aim of creating the WorldBiG binary grid described in the article (link below) was to enable its cooperation with GIS family programs, precise and simple determination of the field surface in any fixed density for the full range of the grid, natural method of coding (labelling) of binary fields, ease of transfer between the systems (connected with the Earth and flat), and finally, easier implementation of the grid in future usable applications of surface "differentiation". All this to facilitate all field analyses in a mathematical and graphic way. Without much effort and unnecessary complications.
A detailed description of the concept of a binary grid can be found in the work entitled "Polska siatka binarnaPolBiG" ( http://maxbot.botany.pl/pubsnew/#article4320 ).
If you do not want to read the whole work (unfortunately, it is in Polish), then a short description of the grid itself with examples, reference grids (kmz, shp), labelling and selfgeneration using the QGIS package can be found here:
Short description of the WorldBiG grid
Look at the figure next to it (PDF). The PolBiG grid with dimensions of 1024×1024 km is developed on a plane tangential to the sphere (with radius R) at the point of connection (Xo, Yo), and the applied mapping f is based on mathematical formulas derived from the Lambert Azimuthal Equal Area Projection model. Reverse transformation f^{ 1} defines the values of geographical coordinates in the WGS 84 reference system for squares of the grid in the rectangular coordinate system (the equivalents of squares are the fields defined as follows after transformation to the ellipsoid WGS 84). In order for this grid to be able to precisely "differentiate" the analysed area and on this basis interesting conclusions can be drawn.
 WorldBiG grid are characterized by the fact that the square of the length of the side of such a grid actually determines the field of the area with such a value.
 A binary grid of 8×8 km marks fields of 64 km^{2}. A 10×10 km grid means 100 km^{2} in the field. For smaller meshes this effect is even more precise.
 WorldBiG grid can be freely compacted. The only limitations are the precision of GPS measurement and terrain (especially in mountainous areas).
 The mesh reduction of the binary grid is very small. During a single compaction stroke the side becomes twice as small and the surface is four times smaller.
 The range of the WorldBiG binary grid is large. It will be possible to carry out analyses with the help of this grid not only in a specific country, but in relatively distant regions.
Applications of binary grid
Botanical research
Apart from creating cartograms, the PolBiG grid will allow for more subtle botanical analyses and description of relations between parameters in relation to the area.
Medical research
Conducting longterm studies of the impact of the environment on humans, or studies of the effectiveness of medicines, depending on where the patients being treated live or work.
Sociological issues
Study of sociological dependencies in the compared areas and study of poverty or social maladjustment in different periods of time in the same area.
Performing analyses for municipalities, districts or cities
These can be services illustrating the pollution of the tested areas or performing other analyses and visualisations for the tested areas (see below).
Genetic research
Contrary to appearances, one can imagine using a binary grid for genetic research ...
This could be the determination of the genetic variability of plants or animals in a limited area. Such tests could be carried out in different periods of time documenting the dynamics of genome variability of the elements selected for testing.
In a similar way, the impact of the variability of the environment itself on the plants or animals in it could be studied. By documenting this and illustrating it graphically in the long term with the help of the WorldBiG grid programming tools.
What can the WorldBiG grid offer to municipalities, districts or cities?
Facilitating the documentation of changes in the studied field parameters, e.g. determining labour migration, construction or sociological issues.
Analysis of cause and effect relationships in the studied area of communes or districts. In particular, the study of the relationship between the existing diseases and pollution.
Compatibility of WorldBiG software with popular QGIS, GoogleEarth and Office systems. This will facilitate visualization and processing of data saved in known formats.
Research and development of data for publications.
An additional tool for academic institutions, universities, researchers and students. It will document the research, facilitate analysis and visualization of field studies.
Research with the help of the WorldBiG grid may concern such scientific fields as forestry, archaeology, botany, geology, resource analysis, sociology, cultural studies, agriculture or pharmacology. Generally, broadly understood field research, for which the grid would enable "differentiation" after analysed parameters.
WorldBiG software can also serve as a useful tool for aggregating data in large databases thanks to its easy adaptation to the formats used. This will allow for the development of analyses in a large time frame for capturing longterm trends.
Start your adventure with the WorldBiG grid
Remember, this version of the WorldBiG grid software is available in a completely free way, regardless of whether it concerns individuals, company employees or researchers. The program generates binary grids adapted to the size of the studied area, labels them and assigns sorted elements to appropriate grid squares, while presenting the obtained surface differentiation results in known formats read by Goole Earth and QGIS software.
Free access for everyone (development version of the programme)
Free access
^{PLN,€,$}0 Always free !
 Divides the area in a binary way
 Facilitates analysis of phenomena on the ground
 Facilitates the creation of cartograms
 Automatically labels the grid
 Groups the elements analysed
The programme is useful?
^{PLN}0 sponsorzy?
 Prosta dokumentacja obliczeń
 Analiza porównawcza
 Możliwe szkolenia i konsultacje
 Filmy i przykłady rozwiązań
 Pomoc w razie konieczności
Własny serwer ?
^{PLN}??? docelowo
 Wszystkie funkcje programu
 Indywidualne administr. serwera
 Uruchomiony backup danych
 Realizacja dodatkowych funkcji
 Praca w sieci lokalnej i zdalnie
Answers to the most common questions
Here we answer the most common questions about the WorldBiG binary grid

In Help, the term 'quantity' is often used. How to understand it ?
This term only emphasizes the fact that it is possible to count in a certain square (mesh) what "fell in" there. These may be specific groups (e.g. plant species), but because there may be several positions in the square containing these specific groups, then we are talking about "group elements", which will be more than the groups themselves. It is worth noting that for a denser grid, the number of positions in the square will be decreasing, and thus the number of groups and their elements in the square (in the extreme case) may be the same.

Why is the WorldBiG grid called binary ?
This term is derived from the simple fact that the maximum size of this grid is set at 1024×1024 km in a rectangular coordinate system. This makes it possible to divide it into smaller squares, gradually in a simple way by dividing the side of a larger square into two identical smaller sides, i.e. the whole larger square into four identical smaller ones. Such division guarantees an even and natural way of compacting the net and makes it easier to label it.

What do you need binary grid labelling for? The determination of geographical coordinates is more accurate and does not require labels.
Yes, it is true, grid squares do not determine the precise location of an element as opposed to geographical coordinates. The label of the square (for a certain density of the grid) is its numerical unambiguous index. This is of great importance to the various databases when dealing with quantities calculated in conjunction with the grid squares. The same label will therefore also be a natural index for these calculated values. It will therefore make it possible to compare data from different databases and possibly establish their links.

What is the difference between a grid with fixed and variable Rradius ?
By choosing a fixed Rradius, the WorldBiG grid is built in exactly the same way for the whole globe. It is assumed that the radius of the Earth is averaged and equal to 6371 km. This is consistent with the distance and surface measurements in Google Earth, but not entirely consistent with reality. However, the error in determining the surface is not great, it does not exceed 0.1% of the surface area.
When you select the variable Rradius option, the program adjusts the size of the radius to bring the sphere's surface as close as possible to the actual surface of the Earth. However, this is only possible with the greatest possible precision at the closest distance to the selected centre point of the grid. This solution is more precise, consistent with the measurements in the QGIS program and ensures the accuracy of surface measurement with an error of 0.002%. Both of these solutions do not take into account hipsometric measurements. 
Can you imagine other nonbinary but similar grids, e.g. decimal ?
Yes, of course. The decimal grid would have a maximum size of 1000×1000 km. All such grids are characterized by the fact that the square of their side length determines the area in the field of exactly this value. Meshes of 8×8 km of the binary grid will form a field of 64 km2. A 10×10 km decimal grid will mark an area of 100 km2. Additionally, both grids are identical at a density of up to 1×1 km. Only the way of labelling in this case will be different.

The grid 64×64 km in Google Earth does not exactly match the grid 1×1 km. In some places the lines are even 20 m away from each other. How to explain it ?
This is due to the way the lines are drawn in Google Earth. The 64×64 km grid corrects the position of lines in the WGS 84 system every 64 km. A 1×1 km grid does this every 1 km. GE program does it in its own way by connecting any two points with the shortest bow. Hence these differences. It is worth noting, however, that in a rectangular system, in which the assignment of elements to appropriate squares takes place, this problem does not occur. It is only a visual effect in Google Earth. The 8×8 km grid view in GE is much more precise. The deviation of the arch is unnoticeable. All the more so for a 1×1 km grid.

What is a binary division of the area with the help of a grid ?
It is a term we use when we "put" on the ground, a grid of appropriate density. Then its "squares" assign the analyzed elements existing in the field to each other. However, since the elements themselves are related to the parameters defining them (e.g. their number in a square, physical and chemical parameters, or e.g. calculable descriptive parameters), such a division of the terrain can be made precisely indirectly on these calculable parameters. Therefore, it is possible to analyse their variability in the terrain, and therefore sometimes also the gradient of this variability.

Why was the Lambert azimuthal projection with an even surface in the WorldBiG binary grid used ?
In this projection, the grid cuts out fields in the studied area very close to quadrangles, the surface of which is, with great accuracy, such as the surface of grid squares in the Cartesian system, and thus the same. This greatly facilitates any numerical analysis and statistical research performed for object parameters. However, the accuracy of the measurements is always slightly lower due to the terrain and the precision of determining geographical coordinates.

Jak uzyskane już ryciny z programu w formacie .pdf lub .dxf można uzupełnić lub poprawić przed przesłaniem ich do publikacji ?
Myślę, że sposobów na to jest co najmniej kilka, ale na pewno warto powiedzieć o dwóch. Jeżeli dysponujemy pakietem Corel Draw to oczywiście można wczytać do tego programu wygenerowany wcześniej z QGIS plik PDF utworzonej ryciny. Drugi sposób może polegać na użyciu dostępnych w każdej chwili programów do edycji plików w formacie PDF: Adobe Acrobat, Acrobat Reader a także narzędzi do edycji PDF  Libre Office.
Some information about us
We deal with the use of the WorldBiG binary grid in science and economy. We hope that the tools shown will be useful.
Marek Verey
Project implementer,physicist by profession
Krzysztof Kochański
Project implementer,by profession a programmer
Johann Heinrich Lambert
mathematician, physicist, philosopher17281777
QGIS software
Multiplatform desktop GIS programhttps://www.qgis.org/
Some information about the above figures
The drawings have been created with the generated PolBiG grid software files using free QGIS and Google Earth systems
1. The workplace
It is worth remembering that in the work of data processing it is good to have an additional monitor which will extend the view of the 'desktop'. This will make it easier to view data and present graphics (G.E. and QGIS).
2. Sample data (Excel format)
View of a simple Excel sheet. It is only necessary to specify names, their geographical location and possible parameters. The server software reads the file and generates the calculation results.
3. Prezentacja w Goole Earth
System obsługi siatki PolBiG umożliwia generowanie binarnych siatek KML, dostosowanych do wielkości badanego terenu. Elementy są przyporządkowane do etykietowanych automatycznie kwadratów.
4. Różna przezroczystość jest miarą liczebności występowania
Im mocniejsze zabarwienie tej samej barwy tym liczebność badanego gatunku jest większa. Widać trzy stopnie zabarwienia.
5. MPN  ukształtowanie terenu
Rycina uzyskana z pomocą pakietu QGIS. Zastosowano podkład WMTScieniowanie (Geoportal). Kolory rozróżniają gatunki znalezione na terenie Magurskiego Parku Narodowego.
6. Różne możliwości prezentacji
QGIS  zastosowano podkład WMTShipsometria z cieniowaniem. Na podkład nałożono trzy grupy "punktów" określające 3 gatunki mchów. W QGIS punkty prezentowane są jako koła, kwadraty i gwiazdki.
7. Badany teren. Kółka proste
Dwu kilometrowa siatka nałożona na cały teren MPN. Kółka reprezentują te kwadraty, w których znalezione zostały stanowiska (pola badawcze). Promień koła jest w ustalonej proporcji z bokiem kwadratu.
8. Teren. Kółka skalowane wg grup
Promień kół jest zróżnicowany i zależny od względnej liczebności grup w kwadratach. Maksymalny zasięg promienia koła można zmieniać używając "skali". Dla 100% skali kółka nigdy nie wychodzą poza kwadrat.
9. Teren. Kółka skalowane elementami
Siatka ta sama, ale promień kół zależy od względnej liczebności elementów w kwadratach całej siatki. W tym przypadku wybrano "skalę" 200%. Zwiększa to różnicę pomiędzy największym i najmniejszym kółkiem.
10. Teren. Skalowanie bezwzględne
Oczka 2x2 km, ale promień koła jest proporcjonalny do bezwzględnej liczebności elementów w kwadracie siatki. Takie rozwiązanie pozwala przykładowo na porównanie tego samego terenu w różnych okresach.
11. Badanie bezwzględne liczebności gatunków MPN w terenie
Wykorzystano dane, w których w sztuczny sposób powielono gatunki w stanowiskach, tak by oddawały pewien rzeczywisty parametr "liczebności" określony przez badaczy. Krycie ustalono na 30%.
12. Podobne badanie z siatką 1/2 km. Krycie: 40%
Wyrażna różnica w wyglądzie "liczebności" dzięki bardziej gęstemu podziałowi siatki. Poprzednio kwadrat #432121234 (2x2 km) "zbierał" wiele stanowisk co zwiększyło bardzo promień koła.
Contact us
We are not yet in the social media. We do not like advertising, nor do we try to promote our ideas in an aggressive way. We prefer indirect communication by email. If you are interested in the method described here you will always contact us :)
Marek Verey
info@podlesie.krakow.pl
+48 501 006 250