# Chaos and Fractals: A Computer Graphical Journey by Clifford A. Pickover

By Clifford A. Pickover

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Subsequen t apical cell divisions in the branch also result in cells that branch. The Antithamnion produces two types of branches t in all three species studied here first type, apparen (Figs. 1, 2, and 3), is opposite determinate branching. These branches are arranged in opposite pairs along the main axis. They are determinate in the sense that they grow to a certain number of cells in length and then cease to grow thereafter. The second type of branch is called indeterminate , and these branches are indeterminate in the sense that they continue to grow more or less indefinitely.

The L-systems presente d here generate images that look very much like the plants they are intended to represent . A comparison of the \. \ • ""V \ \ d by the L-system for A. densum Fig. 2. Image generate (15 iterations). 22 JOHN D . CORBIT and DAVI D J. GARBARY '^^f^^M Fig. 5. Photograp h of an actual specimen oi A. tenuissimum (From A. Athanasiadis , A comparative study of Antithamnion tenuissimum and three varieties of ^4. Crucialum, including var. scandinavicu m var. nov. (Rhodophyceae) . Nord.

Furthermore, it can be clearly seen in Fig. 2b that new capillaries have been formed to supply the tumor with oxygen and glucose. This process is called neovascularization. Thus, further rapid tumor growth is possible. The aim of our work is not only to predict spatial tumor growth but also to simulate and to optimize different kinds of tumor treatment (surgery, radiation and chemotherapy). Thus, algorithms describin^cancer treatment had to be developed [ 8 ], for example by introducing a "Linear Quadratic Model" for computing the number of lethally hit tumor cells as a function of radiation dose rate.