Fibonacci Research Experiment | Luciferin Redux | Fall 2011
During my first semester majoring in Interaction Design at California College of the Arts, I took an interdisciplinary class called Luciferin Redux. It was an intriguing concoction of art design and biology wrapped within the theme of living bioluminescent systems. For a third of the semester, we read about and discussed evolution. We designed visual systems in which complexity can arise from a few simple consistent rules. During the second third of the class, we learned from leading researchers in various biological fields about the systems they were exploring. After the presentations and discussions, we had to use design tools to create systems that function under the same principles as the systems being researched. The final third of the class required us to conceptualize and conduct an experiment on bioluminescent breast-cancer cells.
For my experiment, I wanted to determine if breast-cancer cells divide at the same rate as the Fibonacci Sequence. I also wanted to analyze cell activity on the micro level, and reach a conclusion about how their behavior relative to each other’s locations may affect their division rates. Lastly, I decided to investigate the tool that I used to conduct the research, and determine if the varying sizes of pixels displayed by the imaging algorithm correlates with varying cell-division rates.
I feel as though the clustering of these breast-cancer cells resembles the orbiting of planets around large bodies. Correlations between such systems of nature are evident in the numerous unique ways the Fibonacci Sequence unravels itself. My inspiration and enthusiasm for this experiment stemmed from my humble wonderment of the beguiling mystery surrounding the Fibonacci Sequence. I question how it emerges in so many manifestations of nature and why natural systems produce it.
I conducted the experiment at Stanford Research Lab in Palo Alto.
The first two rows of wells in this petri dish have cell amounts that are arranged in descending order along the starting fibonacci numbers, which are 1,1,2,3,5,8. The first row of cells are submerged in a stagnation medium, which provides limited resources for proliferation. The second row of cells are within a growth medium, which is why their numbers are vastly larger than the cells in the first row of wells. When there are abundant breast-cancer cells clustered together, the colors emitted from the wells are brighter and more vivid. This tends to mostly happen along the partial rings around the middle of the wells. When the clusters get too large, the cells are unable to divide at the same rates. I speculate that is the reason why the middles of the wells are somewhat dimmer than the rings around them. When cells are estranged from the groups, they create less offspring, and enter into a circular, reclusive state.
The work below is a representation of the pixelated image of one of the cell growth wells, specifically, the 5X well, located in the second row, fifth column. I analyzed this particular well because it is a strong representation of both cell growth, and cell reclusion. When compared with the similar looking but refined image underneath it, the imperfections in the square pixels in the larger image become apparent. This is because the research equipment abides by an algorithm which translates the light emitted from the bioluminescent breast-cancer cells into pixels on a strictly patterned matrix.
The pattern of squares and rectangles on the matrix grid goes as follows: 1, 2, 2, 1, 2, 2, 1...
I postulate that the pattern of the matrix has no bearing on cell population count, for that is represented by the pixel brightness, rather than the size of the pixel. I graphed the initial cell amounts to the photon intensities, and I compared the rates of the cells in the growth medium and the cells in the stagnation medium to the fibonacci curve. The results are partially inconclusive, since it is difficult to tell whether the cells will continue to divide at such an exponential rate. However, thus far the breast-cancer cells from both mediums divided at a rate that is remarkably close to the Fibonacci Sequence.
The wondrous Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The Fibonacci sequence follows a single rule: add each number to the number before it in order to reach the next number. I created this mechanistic system to follow the Fibonacci Sequence in various ways. The tokens rotate 45 degrees at each number along the sequence. The tokens are stacked sequentially as they amount to each number of the Fibonacci Sequence as well. The micro-thin line at the end the pinwheel shape is composed of 6765 individual tokens.
When tokens from the merging pinwheels touch, the smaller, thinner ones reflect off the larger, thicker tokens at a 45 degree angle.
After creating a mechanistic system abiding by the Fibonacci Sequence, I designed a generative biological system, represented by the green tadpoles and circles. I reverse engineered the Fibonacci Sequence to determine the rate at which these hypothetical organisms divide and die. Each green tadpole morphs into a circle and divides through mitosis twice in its life, before dying. If every tadpole is able to divide, the population numbers of each successive generation of green organisms will be perfectly reflected in the Fibonacci Sequence.
The tadpoles are placed in a slanted field with a hill and a dip. They are only able to reproduce if there is adequate space for the child tadpoles. If the tadpoles become circles and roll down the field, sometimes they catapolt their newly born tadpoles in the air.