NOVELTY - The downhole tool (10) has first energy interface device (12) which transmits electromagnetic or electrical energy into subsurface material (4), second energy interface device (13) which receives electromagnetic or electrical energy reflected from subsurface material, and processor (11) which estimates property using second electrical signal received from second energy interface device. The first or second energy interface device is fractal-shaped antenna having base motif figure with scaled down replication that changes base motif by linear displacement translation or rotation.    USE - Downhole tool for estimating property, such as resistivity or dielectric constant, of subsurface material, such as earth formation used for e.g. hydrocarbon production, geothermal production, and carbon dioxide sequestration.    ADVANTAGE - Space in downhole tool normally used by wiring can be used for other components since wiring in tool is eliminated because of downhole tool spatial constraints due to the size of the borehole. The use of fractal-shaped antenna increases antenna efficiency, enabling more powerful wireless signal. Because fractal-shaped antenna can be tuned to more than one non-harmonic resonant frequency, communication between different downhole tools in the same drill string can occur simultaneously. Increased efficiency enables the downhole tool to probe deeper into the earth formation. Enables probing various regions of the formation under different conditions requiring different probing frequencies, since fractal-shaped antenna is designed to have number of non-harmonic resonant frequencies.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for estimating property of subsurface material.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of the downhole tool disposed in borehole penetrating the earth.    Subsurface material (4)    Downhole tool (10)    Processor (11)    First energy interface device (12)    Second energy interface device (13)